Skip to main content Accessibility help
×
Hostname: page-component-84b7d79bbc-2l2gl Total loading time: 0 Render date: 2024-07-27T13:58:12.611Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  23 June 2022

Jan van Neerven
Affiliation:
Technische Universiteit Delft, The Netherlands
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Functional Analysis , pp. 693 - 702
Publisher: Cambridge University Press
Print publication year: 2022

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adams, R. A., and Fournier, J. J. F. 2003. Sobolev spaces. 2nd edn. Pure and Applied Mathematics (Amsterdam), vol. 140. Elsevier/Academic Press, Amsterdam. 680, 681Google Scholar
Akhiezer, N. I., and Glazman, I. M. 1981a. Theory of linear operators in Hilbert space. Vol. I. Monographs and Studies in Mathematics, vol. 9. Pitman, Boston, Mass.-London. 680Google Scholar
Akhiezer, N. I., and Glazman, I. M. 1981b. Theory of linear operators in Hilbert space. Vol. II. Monographs and Studies in Mathematics, vol. 10. Pitman, Boston, Mass.-London. 688Google Scholar
Albiac, F., and Kalton, N. J. 2006. Topics in Banach space theory. Graduate Texts in Mathematics, vol. 233. New York: Springer. 673, 675, 677Google Scholar
Aliprantis, C. D., and Burkinshaw, O. 1985. Positive operators. Pure and Applied Mathematics, vol. 119. Academic Press, Inc., Orlando, FL. 673, 675Google Scholar
Allan, G. R., and Ransford, T. J. 1989. Power-dominated elements in a Banach algebra. Studia Math., 94(1), 6379. 677Google Scholar
Amann, H. 1995. Linear and quasilinear parabolic problems, Vol. I: Abstract linear theory. Monographs in Mathematics, vol. 89. Birkhäuser Boston, Inc., Boston, MA. 683CrossRefGoogle Scholar
Amemiya, I., and Araki, H. 1966/1967. A remark on Piron’s paper. Publ. Res. Inst. Math. Sci. Ser. A, 2, 423427. 687Google Scholar
Applebaum, D. 2019. Semigroups of linear operators. London Mathematical Society Student Texts, vol. 93. Cambridge University Press, Cambridge. 683Google Scholar
Arendt, W. 1995. Spectrum and growth of positive semigroups. Pages 21–28 of: Evolution equations (Baton Rouge, LA, 1992). Lecture Notes in Pure and Appl. Math., vol. 168. Dekker, New York. 685Google Scholar
Arendt, W. 2004. Semigroups and evolution equations: functional calculus, regularity and kernel estimates. Pages 1–85 of: Evolutionary equations. Vol. I. Handb. Differ. Equ. North-Holland, Amsterdam. 681, 683Google Scholar
Arendt, W. 2006. Heat kernels. Lecture notes of the 9th Internet Seminar 2005/06, available at www.uni-ulm.de/mawi/iaa/members/arendt/. 681, 683, 684, 686Google Scholar
Arendt, W., and Urban, K. 2010. Partielle Differentialgleichungen: Eine Einführung in analytische und numerische Methoden. Spektrum. 680, 681Google Scholar
Arendt, W., Batty, C. J. K., Hieber, M., and Neubrander, F. 2011. Vector-valued Laplace transforms and Cauchy problems. 2nd edn. Monographs in Mathematics, vol. 96. Birkhäuser/Springer Basel AG, Basel. 683, 685Google Scholar
Arveson, W. 2002. A short course on spectral theory. Graduate Texts in Mathematics, vol. 209. Springer-Verlag, New York. 677, 678, 679CrossRefGoogle Scholar
Atkinson, K., and Han, W. 2009. Theoretical numerical analysis. A functional analysis framework. 3rd edn. Texts in Applied Mathematics, vol. 39. Springer, Dordrecht. 681Google Scholar
Attal, S. 2013. Tensor products and partial traces. Lecture notes, available at math.univlyon1.fr/~attal/. 686Google Scholar
Aupetit, B. 1991. A primer on spectral theory. Universitext. Springer-Verlag, New York. 677Google Scholar
Auscher, P., Hofmann, S., Lacey, M., McIntosh, A., and Tchamitchian, Ph. 2002. The solution of the Kato square root problem for second order elliptic operators on ℝn. Ann. of Math. (2), 156(2), 633654. 686Google Scholar
Axelsson, A., Keith, S., and McIntosh, A. 2006. Quadratic estimates and functional calculi of perturbed Dirac operators. Invent. Math., 163(3), 455497. 686Google Scholar
Baghi, B. 2006. On Nyman, Beurling and Baez–Duarte’s Hilbert space reformulation of the Riemann hypothesis. Proc. Indian Acad. Sci. (Math. Sci.), 116, 137146. 675Google Scholar
Bargmann, V. 1954. On unitary ray representations of continuous groups. Ann. of Math. (2), 59, 146. 689Google Scholar
Beauzamy, B. 1988. Introduction to Operator Theory and Invariant Subspaces. North-Holland Mathematical Library. North-Holland. 675Google Scholar
Beckner, W. 1975. Inequalities in Fourier analysis. Ann. of Math. (2), 102(1), 159182. 676Google Scholar
Bell, J. S. 1966. On the problem of hidden variables in quantum mechanics. Rev. Modern Phys., 38, 447452. 689Google Scholar
Berberian, S. K. 1966. Notes on spectral theory. Van Nostrand Mathematical Studies, No. 5. D. Van Nostrand Co., Inc., Princeton, NJ-Toronto, Ont.-London. 2nd edition by the author available at web.ma.utexas.edu/mp arc/c/09/09-32.pdf. 688Google Scholar
Biegert, M., and Warma, M. 2006. Regularity in capacity and the Dirichlet Laplacian. Potential Anal., 25(3), 289305. 680Google Scholar
Birman, M. Sh. 1989. A proof of the Fredholm trace formula as an application of a simple embedding for kernels integral operators of trace class in L2(ℝm). Report LIT-MATK-R-89-30, Department of Mathematics, Linköpign University. 686Google Scholar
Birman, M. Sh., and Solomjak, M. Z. 1987. Spectral theory of selfadjoint operators in Hilbert space. Mathematics and its Applications (Soviet Series). D. Reidel Publishing Co., Dordrecht. 680Google Scholar
Blackadar, B. 2006. Operator algebras. Encyclopaedia of Mathematical Sciences, vol. 122. Springer-Verlag, Berlin. Theory of C*-algebras and von Neumann algebras, Operator Algebras and Non-commutative Geometry, III. 688Google Scholar
Bleecker, D. D., and Booß Bavnbek, B. 2013. Index theory—with applications to mathematics and physics. International Press, Somerville, MA. 677Google Scholar
Bogachev, V. I. 2007a. Measure theory. Vol. I. Springer-Verlag, Berlin. 675Google Scholar
Bogachev, V. I. 2007b. Measure theory. Vol. II. Springer-Verlag, Berlin. 673CrossRefGoogle Scholar
Bost, J.-B., and Connes, A. 1995. Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory. Selecta Math. (N.S.), 1(3), 411457. 691Google Scholar
Böttcher, A., and Silbermann, B. 2006. Analysis of Toeplitz operators. 2nd edn. Springer Monographs in Mathematics. Springer-Verlag, Berlin. 677Google Scholar
Bratteli, O., and Robinson, D. W. 1987. Operator algebras and quantum statistical mechanics. Vol. 1. 2nd edn. Texts and Monographs in Physics. Springer-Verlag, New York. 688Google Scholar
Brenner, S. C., and Scott, L. R. 2008. The mathematical theory of finite element methods. 3rd edn. Texts in Applied Mathematics, vol. 15. Springer, New York. 681Google Scholar
Bressan, A. 2013. Lecture notes on functional analysis. Graduate Studies in Mathematics, vol. 143. Amer. Math. Soc., Providence, RI. 673, 680Google Scholar
Brezis, H. 2011. Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York. 673, 680, 681Google Scholar
Brislawn, C. 1988. Kernels of trace class operators. Proc. Amer. Math. Soc., 104(4), 11811190.Google Scholar
Brown, A., and Pearcy, C. 1966. Spectra of tensor products of operators. Proc. Amer. Math. Soc., 17, 162166. 690Google Scholar
Busch, P., Grabowski, M., and Lahti, P. J. 1995. Operational quantum physics. Lecture Notes in Physics. New Series m: Monographs, vol. 31. Springer-Verlag, Berlin. 688, 689Google Scholar
Buskes, G. 1993. The Hahn-Banach theorem surveyed. Dissertationes Math., 327, 49. 675Google Scholar
Carleman, T. 1916. Über die Fourierkoeffizienten einer stetigen Funktion. Acta Math., 41(1), 377384. 686Google Scholar
Cartier, P. 1989. A course on determinants. Pages 443–557 of: Conformal invariance and string theory (Poiana Bras¸ov, 1987). Perspect. Phys. Academic Press, Boston, MA. 686Google Scholar
Clément, Ph., and Li, S. 1993/94. Abstract parabolic quasilinear equations and application to a groundwater flow problem. Adv. Math. Sci. Appl., 3 (Special Issue), 1732. 684Google Scholar
Coburn, L. A. 1966. Weyl’s theorem for nonnormal operators. Michigan Math. J., 13, 285288.Google Scholar
Coburn, L. A. 1967. The C*-algebra generated by an isometry. Bull. Amer. Math. Soc., 73, 722726. 677Google Scholar
Connes, A. 1994. Noncommutative geometry. Academic Press, Inc., San Diego, CA. 691Google Scholar
Connes, A., and Consani, C. 2021. The scaling Hamiltonian. J. Operator Theory, 85(1), 257276. 687Google Scholar
Conway, J. B. 1990. A course in functional analysis. 2nd edn. Graduate Texts in Mathematics, vol. 96. Springer-Verlag, New York. 673, 675Google Scholar
Davies, E. B. 1976. Quantum theory of open systems. Academic Press, London-New York. 688Google Scholar
Davies, E. B. 1980. One-parameter semigroups. London Mathematical Society Monographs, vol. 15. Academic Press, Inc., London-New York. 679, 683Google Scholar
De Simon, L. 1964. Un’applicazione della teoria degli integrali singolari allo studio delle equazioni differenziali lineari astratte del primo ordine. Rend. Sem. Mat. Univ. Padova, 34, 205223. 683Google Scholar
Diestel, J. 1984. Sequences and series in Banach spaces. Graduate Texts in Mathematics, vol. 92. Springer-Verlag, New York. 673Google Scholar
Diestel, J., and Uhl, J. J. Jr. 1977. Vector measures. Providence, RI: Amer. Math. Soc. 673, 677Google Scholar
Dieudonné, J. 1981. History of functional analysis. North-Holland Mathematics Studies, vol. 49. North-Holland Publishing Co., Amsterdam-New York. 673Google Scholar
Douglas, R. G. 1998. Banach algebra techniques in operator theory. 2nd edn. Graduate Texts in Mathematics, vol. 179. Springer-Verlag, New York. 677Google Scholar
van Dulst, D. 1989. Characterizations of Banach spaces not containing ℓ1. CWI Tract, vol. 59. Amsterdam: CWI. 677Google Scholar
Dunford, N., and Schwartz, J. T. 1988a. Linear operators. Part I: General theory. Wiley Classics Library. John Wiley & Sons, Inc., New York. Reprint of the 1958 original. 673Google Scholar
Dunford, N., and Schwartz, J. T. 1988b. Linear operators. Part II: Spectral theory, selfadjoint operators in Hilbert space. Wiley Classics Library. John Wiley & Sons, Inc., New York. Reprint of the 1963 original. 677, 680, 686Google Scholar
Duoandikoetxea, J. 2001. Fourier analysis. Graduate Studies in Mathematics, vol. 29. Amer. Math. Soc., Providence, RI. Translated and revised from the 1995 Spanish original. 676Google Scholar
Edmunds, D. E., and Evans, W. D. 2018a. Elliptic differential operators and spectral analysis. Springer Monographs in Mathematics. Springer, Cham. 681Google Scholar
Edmunds, D. E., and Evans, W. D. 2018b. Spectral theory and differential operators. 2nd edn. Oxford Mathematical Monographs. Oxford University Press, Oxford. 680, 681Google Scholar
Einsiedler, M., and Ward, Th. 2017. Functional analysis, spectral theory, and applications. Graduate Texts in Mathematics, vol. 276. Springer, Cham. 673Google Scholar
Engel, K.-J., and Nagel, R. 2000. One-parameter semigroups for linear evolution equations. Graduate Texts in Mathematics, vol. 194. New York: Springer-Verlag. 683Google Scholar
Epperson, J. B. 1989. The hypercontractive approach to exactly bounding an operator with complex Gaussian kernel. J. Funct. Anal., 87(1), 130. 685Google Scholar
Evans, L. C. 2010. Partial differential equations. 2nd edn. Graduate Studies in Mathematics, vol. 19. Amer. Math. Soc., Providence, RI. 680, 681Google Scholar
Filonov, N. 2005. On an inequality between Dirichlet and Neumann eigenvalues for the Laplace operator. St. Petersburg Math. J., 16(2), 413416. 682Google Scholar
Foguel, S. R. 1958. On a theorem by A. E. Taylor. Proc. Amer. Math. Soc., 9, 325. 675Google Scholar
Folland, G. B. 1989. Harmonic analysis in phase space. Annals of Mathematics Studies, vol. 122. Princeton University Press, Princeton, NJ. 690Google Scholar
Folland, G. B. 1999. Real analysis. 2nd edn. Pure and Applied Mathematics (New York). New York: John Wiley & Sons Inc. 675, 691Google Scholar
Folland, G. B. 2016. A course in abstract harmonic analysis. 2nd edn. Textbooks in Mathematics. CRC Press, Boca Raton, FL. 678, 689Google Scholar
Fremlin, D. H. 2015. Measure theory. Vol. 5. Set-theoretic measure theory. Part I. Torres Fremlin, Colchester. Corrected reprint of the 2008 original. 674Google Scholar
Friedlander, L. 1991. Some inequalities between Dirichlet and Neumann eigenvalues. Arch. Ration. Mech. Anal., 116(2), 153160. 682Google Scholar
Funano, K. 2022. A note on domain monotonicity for the Neumann eigenvalues of the Laplacian. arXiv:2202.03598. 682Google Scholar
Garrison, J. C., and Wong, J. 1970. Canonically conjugate pairs, uncertainty relations, and phase operators. J. Mathematical Phys., 11, 22422249. 688Google Scholar
Gelfand, I. M. 1941. Zur Theorie der Charaktere der Abelschen topologischen Gruppen. Mat. Sbornik N. S., 51, 4950. 677Google Scholar
Gilbarg, D., and Trudinger, N. S. 2001. Elliptic partial differential equations of second order. Classics in Mathematics. Springer-Verlag, Berlin. Reprint of the 1998 edition. 681Google Scholar
Gohberg, I., Goldberg, S., and Kaashoek, M. 2003. Basic classes of linear operators. Birkhäuser. 675Google Scholar
Gohberg, I., Goldberg, S., and Kaashoek, M. A. 2013. Classes of linear operators. Operator Theory: Advances and Applications, vol. 63. Birkhäuser. 675Google Scholar
Gordon, C., Webb, D. L., and Wolpert, S. 1992. One cannot hear the shape of a drum. Bull. Amer. Math. Soc. (N.S.), 27(1), 134138. 681Google Scholar
Grafakos, L. 2008. Classical Fourier analysis. 2nd edn. Graduate Texts in Mathematics, vol. 249. New York: Springer. 676Google Scholar
Grebenkov, D. S., and Nguyen, B.-T. 2013. Geometrical structure of Laplacian eigenfunctions. SIAM Review, 55(4), 601667. 681Google Scholar
Grieser, D. 2007. Über Eigenwerte, Integrale und : die Idee der Spurformel. Math. Semesterber., 54(2), 199217. 686Google Scholar
Gustafson, K. E., and Rao, D. K. M. 1997. Numerical range. Universitext. Springer-Verlag, New York. 679Google Scholar
Haase, M. H. A. 2007. Convexity inequalities for positive operators. Positivity, 11(1), 5768. 673Google Scholar
Haase, M. H. A. 2018. Functional calculus. Lecture notes of the 21st Internet Seminar, available at www.math.uni-kiel.de/isem21. 679Google Scholar
Hall, B. C. 2013. Quantum theory for mathematicians. Graduate Texts in Mathematics, vol. 267. Springer, New York. 687, 690Google Scholar
Han, D., Larson, D. R., Liu, B., and Liu, R. 2014. Operator-valued measures, dilations, and the theory of frames. Mem. Amer. Math. Soc., 229(1075). 688Google Scholar
Hanche-Olsen, H., Holden, H., and Malinnikova, E. 2019. An improvement of the Kolmogorov–Riesz compactness theorem. Expositiones Math., 37(1), 8491. 673Google Scholar
Helton, J. W., and Howe, R. E. 1973. Integral operators: commutators, traces, index and homology. Pages 141–209. Lecture Notes in Math., Vol. 345 of: Proceedings of a Conference Operator Theory (Dalhousie Univ., Halifax, N.S., 1973). 686Google Scholar
Henrot, A. 2006. Extremum problems for eigenvalues of elliptic operators. Frontiers in Mathematics. Birkhäuser Verlag, Basel. 681Google Scholar
Heunen, C., and Kornell, A. 2022. Axioms for the category of Hilbert spaces. Proceedings of the National Academy of Sciences, 119(9), e2117024119. 687Google Scholar
Heuser, H. 2006. Funktionalanalysis. 4th edn. Mathematische Leitfäden. B. G. Teubner, Stuttgart. 679Google Scholar
Higson, N. 2004. The local index formula in noncommutative geometry. Pages 443–536 of: Contemporary developments in algebraic K-theory. ICTP Lect. Notes, XV. Abdus Salam Int. Cent. Theoret. Phys., Trieste. 681Google Scholar
Hille, E., and Phillips, R. S. 1957. Functional analysis and semi-groups. Amer. Math. Soc. Colloq. Publ., vol. 31. Providence, RI: Amer. Math. Soc. rev. ed. 683Google Scholar
Holevo, A. 2011. Probabilistic and statistical aspects of quantum theory. 2nd edn. Quaderni/Monographs, vol. 1. Edizioni della Normale, Pisa. 688, 689Google Scholar
Holland, S. S. Jr. 1995. Orthomodularity in infinite dimensions; a theorem of M. Solèr. Bull. Amer. Math. Soc. (N.S.), 32(2), 205234. 687Google Scholar
Hundertmark, D., Machinek, L., Meyries, M., and Schnaubelt, R. 2013. Operator semigroups and dispersive equations. Lecture notes of the 16th Internet Seminar 2012/13, available at isem.math.kit.edu. 685Google Scholar
Hytönen, T. P., van Neerven, J. M. A. M., Veraar, M. C., and Weis, L. W. 2016. Analysis in Banach spaces. Vol. I: Martingales and Littlewood-Paley theory. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, vol. 63. Springer, Cham. 673, 674, 676, 680Google Scholar
Hytönen, T. P., van Neerven, J. M. A. M, Veraar, M. C., and Weis, L. W. 2017. Analysis in Banach spaces. Vol. II: Probabilistic methods and operator theory. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, vol. 67. Springer, Cham. 683Google Scholar
Hytönen, T. P., van Neerven, J. M. A. M., Veraar, M. C., and Weis, L. W. 2022+. Analysis in Banach spaces. Vol. III: Harmonic analysis and operator theory. In preparation. 676, 683Google Scholar
Hytönen, T. P., van Neerven, J. M. A. M., Veraar, M. C., and Weis, L. W. 2023+. Analysis in Banach spaces. Vol. IV: Stochastic analysis. In preparation. 684Google Scholar
Janson, S. 1997. Gaussian Hilbert spaces. Cambridge Tracts in Mathematics, vol. 129. Cambridge: Cambridge University Press. 684, 690Google Scholar
Jech, Th. J. 1973. The axiom of choice. North-Holland, Amsterdam-London. Studies in Logic and the Foundations of Mathematics, Vol. 75. 691Google Scholar
Jech, Th. J. 2003. Set theory. Springer Monographs in Mathematics. Springer-Verlag, Berlin. Third edition. 691Google Scholar
Jorgensen, P. 1982. Spectral theory for infinitesimal generators of one-parameter groups of isometries: The min-max principle and compact perturbations. J. Math. Anal. Appl., 90, 343370. 683Google Scholar
Jost, J. 2013. Partial differential equations. 3rd edn. Graduate Texts in Mathematics, vol. 214. Springer, New York. 680Google Scholar
Kac, M. 1966. Can one hear the shape of a drum? Amer. Math. Monthly, 73(4, part II), 123. 681Google Scholar
Kallenberg, O. 2002. Foundations of modern probability. 2nd edn. Probability and its Applications (New York). Springer-Verlag, New York. 691Google Scholar
Kato, T. 1961. Fractional powers of dissipative operators. J. Math. Soc. Japan, 13, 246274. 686Google Scholar
Kato, T. 1995. Perturbation theory for linear operators. Classics in Mathematics. Springer-Verlag, Berlin. Reprint of the 1980 edition. 680, 681Google Scholar
Koelink, H. T. 1996. 8 Lectures on quantum groups and q-special functions. arXiv:q-alg/9608018. 679Google Scholar
Krylov, N. V. 2008. Lectures on elliptic and parabolic equations in Sobolev spaces. Graduate Studies in Mathematics, vol. 96. Amer. Math. Soc., Providence, RI. 680, 681Google Scholar
Landsman, N. P. 1998. Mathematical topics between classical and quantum mechanics. Springer Monographs in Mathematics. Springer-Verlag, New York. 687, 688Google Scholar
Landsman, N. P. 2017. Foundations of quantum theory. Fundamental Theories of Physics, vol. 188. Springer, Cham. 687, 688, 689CrossRefGoogle Scholar
Landsman, N. P. 2019. Quantum theory and functional analysis. arXiv:1911.06630. 687Google Scholar
Lax, P. D. 2002. Functional Analysis. Wiley. 673Google Scholar
Levine, H. A., and Weinberger, H. F. 1986. Inequalities between Dirichlet and Neumann eigenvalues. Arch. Ration. Mech. Anal., 94(3), 193208. 682Google Scholar
Li, C.-K. 1994. C-numerical ranges and C-numerical radii. Linear and Multilinear Algebra, 37(1-3), 5182. 679Google Scholar
Li, D., and Queffélec, H. 2004. Introduction à l’étude des espaces de Banach. Cours Spécialisés, vol. 12. Société Mathématique de France, Paris. 673Google Scholar
Lindenstrauss, J., and Tzafriri, L. 1971. On the complemented subspaces problem. Israel J. Math., 9, 263269. 674Google Scholar
Lunardi, A. 1995. Analytic semigroups and optimal regularity in parabolic problems. Progress in Nonlinear Differential Equations and their Applications, vol. 16. Birkhäuser, Basel. 683Google Scholar
Luxemburg, W. A. J., and Zaanen, A. C. 1971. Riesz spaces. North-Holland. 673Google Scholar
Maas, J., and van Neerven, J. M. A. M. 2009. Boundedness of Riesz transforms for elliptic operators on abstract Wiener spaces. J. Funct. Anal., 257(8), 24102475. 684CrossRefGoogle Scholar
Mackey, G. W. 1968. Induced representations of groups and quantum mechanics. W. A. Benjamin, Inc., New York-Amsterdam; Boringhieri, Turin. 687, 689Google Scholar
Maligranda, L. 1997. On the norms of operators in the real and the complex case. Pages 67–71 of: Seminar on Banach spaces and related topics: 14/12/1997-14/12/1997. 676Google Scholar
McIntosh, A. 1982. On representing closed accretive sesquilinear forms as (A1/2u, A*1/2v). Pages 252–267 of: Nonlinear partial differential equations and their applications. Collège de France Seminar, Vol. III (Paris, 1980/1981). Res. Notes in Math., vol. 70. Pitman, Boston, Mass.-London. 686Google Scholar
Mercer, J. 1909. Functions of positive and negative type, and their connection to the theory of integral equations. Phil. Trans. Royal Soc. London. Series A, 209(441-458), 415446. 686Google Scholar
Metafune, G., Prüss, J., Rhandi, A., and Schnaubelt, R. 2002. The domain of the Ornstein–Uhlenbeck operator on an Lp-space with invariant measure. Ann. Scuola Norm.-Sci, 1(2), 471485. 684Google Scholar
Meyer-Nieberg, P. 1991. Banach lattices. Universitext. Berlin: Springer-Verlag. 673Google Scholar
Monna, A. F. 1973. Functional analysis in historical perspective. John Wiley & Sons, New York-Toronto, Ont. 673Google Scholar
Müller, V. 2007. Spectral theory of linear operators and spectral systems in Banach algebras. 2nd edn. Operator Theory: Advances and Applications, vol. 139. Birkhäuser, Basel. 677Google Scholar
Murphy, G. J. 1994. Fredholm index theory and the trace. Proc. Roy. Irish Acad. Sect. A, 94(2), 161166. 686, 687Google Scholar
Musiał, K. 2002. Pettis integral. Pages 531–586 of: Handbook of measure theory, Vol. I, II. Amsterdam: North-Holland. 677Google Scholar
van Neerven, J. M. A. M. 1997. Elementary operator-theoretic proof of Wiener’s Tauberian Theorem. Rendic. Istit. Matem. Univ. Trieste Suppl. Vol. XXVIII, 281286. 683Google Scholar
van Neerven, J. M. A. M., and Portal, P. 2018. The Weyl calculus with respect to the Gaussian measure and restricted Lp-Lq boundedness of the Ornstein-Uhlenbeck semigroup in complex time. Bull. Soc. Math. France, 146(4), 691712. 685, 690Google Scholar
van Neerven, J. M. A. M., Veraar, M. C., and Weis, L. W. 2015. Stochastic integration in Banach spaces – a survey. In: Stochastic analysis: A series of lectures. Progress in Probability, vol. 68. Birkhäuser Verlag. 674Google Scholar
Nikolski, N. K. 2002. Operators, functions, and systems: an easy reading, Vol. 1. Mathematical Surveys and Monographs, vol. 92. Amer. Math. Soc., Providence, RI. 675, 677Google Scholar
Nualart, D. 2006. The Malliavin calculus and related topics. 2nd edn. Probability and its Applications (New York). Springer-Verlag, Berlin. 684, 690Google Scholar
Osgood, W. F. 1903. A Jordan curve of positive area. Trans. Amer. Math. Soc., 4(1), 107112. 681Google Scholar
Ouhabaz, E. M. 2005. Analysis of heat equations on domains. London Mathematical Society Monographs Series, vol. 31. Princeton University Press, Princeton, NJ. 681Google Scholar
Parthasarathy, K. R. 1992. An introduction to quantum stochastic calculus. Modern Birkhäuser Classics. Birkhäuser/Springer Basel AG, Basel. 2012 reprint of the 1992 original. 690Google Scholar
Parthasarathy, K. R. 2005. Mathematical foundations of quantum mechanics. Texts and Readings in Mathematics, vol. 35. New Delhi: Hindustan Book Agency. 687, 688, 689Google Scholar
Paulsen, V. 2002. Completely bounded maps and operator algebras. Cambridge Studies in Advanced Mathematics, vol. 78. Cambridge University Press, Cambridge. 688Google Scholar
Pazy, A. 1983. Semigroups of linear operators and applications to partial differential equations. Applied Math. Sciences, vol. 44. New York: Springer-Verlag. 683Google Scholar
Pedersen, G. K. 2018. C*-algebras and their automorphism groups. Pure and Applied Mathematics (Amsterdam). Academic Press, London. 679, 688Google Scholar
Pettis, B. J. 1938. On integration in vector spaces. Trans. Amer. Math. Soc., 44(2), 277304. 676Google Scholar
Phelps, R. R. 1960. Uniqueness of Hahn-Banach extensions and unique best approximation. Trans. Amer. Math. Soc., 95, 238255. 675Google Scholar
Phillips, R. S. 1955. The adjoint semi-group. Pac. J. Math., 5, 269283. 683Google Scholar
Pietsch, A. 2007. History of Banach spaces and linear operators. Boston, MA: Birkhäuser Boston Inc. 673, 675Google Scholar
Piron, C. 1964. Axiomatique quantique. Helv. Phys. Acta, 37, 439468. 687Google Scholar
Pisier, G. 2016. Martingales in Banach spaces. Cambridge Studies in Advanced Mathematics, vol. 155. Cambridge University Press. 674Google Scholar
Reed, M., and Simon, B. 1975. Methods of modern mathematical physics. Vol. II: Fourier analysis, self-adjointness. New York: Academic Press. 680Google Scholar
Riesz, M. 1926. Sur les maxima des formes bilinéaires et sur les fonctionnelles linéaires. Acta Math., 49(3-4), 465497. 676Google Scholar
Rosenberg, J. 2004. A selective history of the Stone-von Neumann theorem. Pages 331–353 of: Operator algebras, quantization, and noncommutative geometry. Contemp. Math., vol. 365. Amer. Math. Soc., Providence, RI. 690Google Scholar
Rubin, H., and Rubin, J. E. 1970. Equivalents of the axiom of choice. Studies in Logic and the Foundations of Mathematics. North-Holland Publishing Co., Amsterdam-London. 691Google Scholar
Rudin, W. 1987. Real and complex analysis. 3rd edn. McGraw-Hill Book Co., New York. 674, 677, 679Google Scholar
Rudin, W. 1991. Functional analysis. 2nd edn. International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York. 673, 675, 678, 679, 680, 688Google Scholar
Ruzhansky, M., and Turunen, V. 2010. Pseudo-differential operators and symmetries. Pseudo-Differential Operators. Theory and Applications, vol. 2. Birkhäuser Verlag, Basel. 675, 691Google Scholar
Ryan, R. A. 2002. Introduction to tensor products of Banach spaces. Springer Monographs in Mathematics. Springer-Verlag London, Ltd., London. 677, 691Google Scholar
Safarov, Yu., and Vassilev, D. 1997. The asymptotic distribution of eigenvalues of partial differential operators. Transl. Math. Monogr., vol. 155. Amer. Math. Soc., Providence, RI. 682Google Scholar
Schaefer, H. H. 1974. Banach lattices and positive operators. Grundlehren der Mathematischen Wissenschaften, vol. 215. New York: Springer-Verlag. 673Google Scholar
Schechter, M. 2002. Principles of functional analysis. 2nd edn. Graduate Studies in Mathematics, vol. 36. Amer. Math. Soc., Providence, RI. 673, 677Google Scholar
Schmüdgen, K. 2012. Unbounded self-adjoint operators on Hilbert space. Graduate Texts in Mathematics, vol. 265. Springer, Dordrecht. 680Google Scholar
Seeley, R. T. 1964. Extension of C functions defined in a half space. Proc. Amer. Math. Soc., 15, 625626. 680Google Scholar
Segal, I. E. 1956. Tensor algebras over Hilbert spaces. I. Trans. Amer. Math. Soc., 81, 106134. 690Google Scholar
Simon, B. 1974. The P(φ)2 Euclidean (quantum) field theory. Princeton Series in Physics. Princeton University Press, Princeton, NJ. 690Google Scholar
Simon, B. 1977. Notes on infinite determinants of Hilbert space operators. Adv. Math., 24(3), 244273. 686Google Scholar
Simon, B. 2005. Trace ideals and their applications. 2nd edn. Mathematical Surveys and Monographs, vol. 120. American Mathematical Soc. 686Google Scholar
Sobczyk, A. 1941. Projection of the space (m) on its subspace (c0). Bull. Amer. Math. Soc., 47, 938947. 675Google Scholar
Solèr, M. P. 1995. Characterization of Hilbert spaces by orthomodular spaces. Comm. Algebra, 23(1), 219243. 687Google Scholar
Stein, E. M. 1970. Singular integrals and differentiability properties of functions. Princeton Mathematical Series, No. 30. Princeton University Press, Princeton, NJ. 673, 676Google Scholar
Stein, E. M. 1993. Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals. Princeton University Press. 676Google Scholar
Stein, E. M., and Shakarchi, R. 2011. Functional analysis. Princeton University Press, Princeton, NJ. Volume 4 of Princeton Lectures in Analysis. 685Google Scholar
Sternberg, S. 1994. Group theory and physics. Cambridge University Press, Cambridge. 689Google Scholar
Stinespring, W. F. 1955. Positive functions on C*-algebras. Proc. Amer. Math. Soc., 6, 211216. 688Google Scholar
Sz.-Nagy, B. 1967. Spektraldarstellung linearer Transformationen des Hilbertschen Raumes. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 39. Springer-Verlag, Berlin-New York. 680Google Scholar
Takesaki, M. 2002. Theory of operator algebras. I. Encyclopaedia of Mathematical Sciences, vol. 124. Springer-Verlag, Berlin. Reprint of the first (1979) edition, Operator Algebras and Non-commutative Geometry, 5. 688Google Scholar
Takhtajan, L. A. 2008. Quantum mechanics for mathematicians. Graduate Studies in Mathematics, vol. 95. Amer. Math. Soc., Providence, RI. 687Google Scholar
Talagrand, M. 1984. Pettis integral and measure theory. Mem. Amer. Math. Soc., 51(307). 677Google Scholar
Talagrand, M. 2022. What is a quantum field theory? Cambridge University Press. 690Google Scholar
Tanabe, H. 1979. Equations of evolution. Monographs and Studies in Mathematics, vol. 6. Pitman, Boston, Mass.-London. 683Google Scholar
Taylor, A. E. 1939. The extension of linear functionals. Duke Math. J., 5, 538547. 675Google Scholar
Terzioğglu, T. 1971. A characterization of compact linear mappings. Arch. Math. (Basel), 22, 7678. 677Google Scholar
Unterberger, A. 1979. Oscillateur harmonique et opérateurs pseudo-différentiels. Ann. Inst. Fourier (Grenoble), 29(3), xi, 201221. 690Google Scholar
Varadarajan, V. S. 1985. Geometry of quantum theory. 2nd edn. New York: Springer-Verlag. 689Google Scholar
von Neumann, J. 1968. Mathematische Grundlagen der Quantenmechanik. Grundlehren der mathematischen Wissenschaften, vol. 38. Springer-Verlag, Berlin-New York. Reprint of the first edition, 1932. 687Google Scholar
Werner, D. 2000. Funktionalanalysis. 3rd edn. Springer-Verlag, Berlin. 673Google Scholar
Whitley, R. 1968. The spectral theorem for a normal operator. Amer. Math. Monthly, 75, 856861. 679Google Scholar
Woit, P. 2017. Quantum theory, groups and representations. Springer, Cham. An introduction. 689Google Scholar
Yosida, K. 1980. Functional analysis. 6th edn. Grundlehren der Mathematischen Wissenschaften, vol. 123. Springer-Verlag, Berlin-New York. 673Google Scholar
Zaanen, A. C. 1997. Introduction to operator theory in Riesz spaces. Springer-Verlag, Berlin. 673Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Jan van Neerven, Technische Universiteit Delft, The Netherlands
  • Book: Functional Analysis
  • Online publication: 23 June 2022
  • Chapter DOI: https://doi.org/10.1017/9781009232487.025
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Jan van Neerven, Technische Universiteit Delft, The Netherlands
  • Book: Functional Analysis
  • Online publication: 23 June 2022
  • Chapter DOI: https://doi.org/10.1017/9781009232487.025
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Jan van Neerven, Technische Universiteit Delft, The Netherlands
  • Book: Functional Analysis
  • Online publication: 23 June 2022
  • Chapter DOI: https://doi.org/10.1017/9781009232487.025
Available formats
×