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META-CENTRALIZERS OF NON-LOCALLY COMPACT GROUP ALGEBRAS

Part of: Abstract harmonic analysis Topological and differentiable algebraic systems General nonassociative rings

Published online by Cambridge University Press:  18 December 2014

S. V. LUDKOVSKY
S. V. LUDKOVSKY*
Affiliation:
Department of Applied Mathematics, Moscow State Technical University MIREA, av. Vernadsky 78, Moscow 119454, Russia e-mail: sludkowski@mail.ru
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Abstract

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Meta-centralizers of non-locally compact group algebras are studied. Theorems about their representations with the help of families of generalized measures are proved. Isomorphisms of group algebras are investigated in relation with meta-centralizers.

MSC classification

Primary: 17A01: General theory
Secondary: 17A99: None of the above, but in this section 22A10: Analysis on general topological groups 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc. 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 57 , Issue 2 , May 2015 , pp. 349 - 364
Copyright
Copyright © Glasgow Mathematical Journal Trust 2014 

References

REFERENCES

1.Dunford, N. and Schwartz, J. C., Linear operators. vol. 1–3 (John Wiley and Sons, Inc., New York, USA, 1966).Google Scholar
2.Banaszczyk, W., Additive subgroups of topological vector spaces, Lecture Notes in Mathematics, vol. 1466 (Spinger-Verlag, Berlin, USA, 1991).Google Scholar
3.Banaszczyk, W., On the existence of exotic Banach-Lie groups, Math. Ann. 264 (4) (1983), 485–493.Google Scholar
4.Belopolskaya, Ya. I. and Dalecky, Yu. L., Stochastic equations and differential geometry (Kluwer Academic Publishers, Dordrecht, 1989).Google Scholar
5.Bogachev, V. I., Measure theory. vol. 1, 2 (Springer-Verlag, Berlin, USA, 2007).Google Scholar
6.Bourbaki, N., Integration. Vector integration. Haar measure. Convolution and representations (Moscow, Nauka, 1970), Ch. 6–8.Google Scholar
7.Dalecky, Yu. L. and Fomin, S. V., Measures and differential equations in infinite-dimensional spaces (Kluwer Academic Publishers, Dordrecht, 1991).Google Scholar
8.Dalecky, Yu. L. and Shnaiderman, Ya. L., Diffusion and quasi-invariant measures on infinite-dimensional Lie groups, Funct. Anal. Appl. 3 (2) (1969), 156–158.Google Scholar
9.Engelking, R., General topology (Moscow, Mir, 1986).Google Scholar
10.Fell, J. M. G. and Doran, R. S., Representations of *-algebras, locally compact groups, and Banach *-algebraic bundles (Boston, Academic Press, 1988).Google Scholar
11.Fidaleo, F., Continuity of Borel actions of Polish groups on standard measure algebras, Atti Sem. Mat. Fiz. Univ. Modena 48 (1) (2000), 79–89.Google Scholar
12.Ghahramani, F., Runde, V. and Willis, G., Derivations on group algebras, Proc. London Math. Soc. 80 (2) (2000), 360–390.CrossRefGoogle Scholar
13.Hewitt, E. and Ross, K. A., Abstract harmonic analysis. vol. 1, 2 (Springer-Verlag, Berlin, USA, 1994).Google Scholar
14.Isbell, J. R., Uniform spaces, Mathematical Surveys, No. 12 (American Mathematical Society, Providence, RI, 1964).CrossRefGoogle Scholar
15.Johnson, B. E., The derivation problem for group algebras of connected locally compact groups, J. London Math. Soc. 63 (2) (2001), 441–452.Google Scholar
16.Kawada, Y., On the group ring of a topological group, Math. Japonicae 1 (1) (1948), 1–5.Google Scholar
17.Kolmogorov, A. N. and Fomin, S. V., Elements of theory of functions and functional analysis (Moscow, Nauka, 1989).Google Scholar
18.Losert, V., The derivation problem for group algebras, Annals of Math. 168 (1) (2008), 221–246.Google Scholar
19.Ludkovsky, S. V.Operators on a non locally compact group algebra, Bull. Sci. Math.(Paris). Ser.2 137 (5) (2013), 557–573; DOI: 10.1016/j.bulsci.2012.11.008CrossRefGoogle Scholar
20.Ludkovsky, S. V., Topological transformation groups of manifolds over non-Archimedean fields, representations and quasi-invariant measures, I, J. Math. Sci., N.Y. (Springer) 147 (3) (2008), 6703–6846.Google Scholar
21.Ludkovsky, S. V., Topological transformation groups of manifolds over non-Archimedean fields, representations and quasi-invariant measures, II J. Math. Sci., N.Y. (Springer) 150 (4) (2008), 2123–2223.Google Scholar
22.Ludkovsky, S. V., Stochastic processes on geometric loop groups, diffeomorphism groups of connected manifolds, associated unitary representations, J. Math. Sci., N.Y. (Springer) 141 (3) (2007), 1331–1384.Google Scholar
23.Ludkovsky, S. V., Quasi-invariant measures on a group of diffeomorphisms of an infinite-dimensional real manifold and induced irreducible unitary representations, Rend. dell'Istituto di Matem. dell'Università di Trieste. Nuova Serie. 30 (1–2) (1999), 101–134.Google Scholar
24.Ludkovsky, S. V., Properties of quasi-invariant measures on topological groups and associated algebras, Ann. Math. B. Pascal. 6 (1) (1999), 33–45.CrossRefGoogle Scholar
25.Ludkovsky, S. V., Semidirect products of loops and groups of diffeomorphisms of real, complex and quaternion manifolds, and their representations, in Focus on Groups Theory Research (Ying, L. M., Editor) (Nova Science Publishers, Inc., New York, 2006), 59–136.Google Scholar
26.Naimark, M. A., Normed Rings (Moscow, Nauka, 1968).Google Scholar
27.Narici, L. and Beckenstein, E., Topological vector spaces (Marcel-Dekker Inc., New York, USA, 1985).Google Scholar
28.Varadarajan, V. S., Measures on topological spaces Mat. Sbornik. 55 (1961), 35–100 (in Russian); English transl.: Amer. Math. Soc. Transl. 48 (2) (1965), 161–228.Google Scholar
29.Wendel, J. G., Left centralizers and isomorphisms of group algebras, Pac.J. Math. 2 (2) (1952), 251–261.Google Scholar