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Projections in the Convex Hull of Surjective Isometries

Published online by Cambridge University Press:  20 November 2018

Fernanda Botelho
Affiliation:
Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152 e-mail: mbotelho@memphis.edujjamison@memphis.edu
James Jamison
Affiliation:
Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152 e-mail: mbotelho@memphis.edujjamison@memphis.edu
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Abstract

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We characterize those linear projections represented as a convex combination of two surjective isometries on standard Banach spaces of continuous functions with values in a strictly convex Banach space.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2010

References

[1] Behrends, E., M-structure and the Banach–Stone Theorem. Lecture Notes in Mathematics, 736, Springer, Berlin, 1979.Google Scholar
[2] Berkson, E., Hermitian projections and orthogonality in Banach spaces. Proc. London Math. Soc. (3) 24(1972), 101118. doi:10.1112/plms/s3-24.1.101Google Scholar
[3] Bernau, S. J. and Lacey, H. E., Bicontractive projections and reordering of Lp-Spaces. Pacific J. Math. 69(1977), no. 2, 291302.Google Scholar
[4] Botelho, F. and Jamison, J. E., Generalized bi-circular projections on , X. Rocky Mountain J. Math. 40(2010), no. 1, 7783. doi:10.1216/RMJ-2010-40-1-77Google Scholar
[5] Botelho, F. and Jamison, J. E., Generalized bi-circular projections on minimal ideals of operators. Proc. Amer. Math. Soc. 136(2008), no. 4, 13971402. doi:10.1090/S0002-9939-07-09134-4Google Scholar
[6] Friedman, Y. and Russo, B., Contractive projections on C 0(K) . Trans. Amer. Math. Soc. 273(1982), no. 1, 5773. doi:10.2307/1999192Google Scholar
[7] Fleming, R. J. and Jamison, J. E., Isometries on Banach Spaces: function spaces, Chapman & Hall, Boca Raton, FL, 2003.Google Scholar
[8] Jerison, M., The space of bounded maps into a Banach space. Ann. of Math. (2) 52(1950), 309327. doi:10.2307/1969472Google Scholar
[9] Fosner, M., Ilisevic, D., and Li, C., G-invariant norms and bicircular projections. Linear Algebra Appl. 420(2007), no. 2–3, 596608. doi:10.1016/j.laa.2006.08.014Google Scholar
[10] Jamison, J. E., Bicircular projections on some Banach spaces. Linear Algebra Appl. 420(2007), no. 1, 2933. doi:10.1016/j.laa.2006.05.009Google Scholar
[11] Spain, P. G., Ultrahermitian projections on Banach spaces. http://www.maths.gla.ac.uk/»pgs/pubs.htm Google Scholar
[12] Stachó, L. L. and Zalar, B., Bicircular projections on some matrix and operator spaces. Linear Algebra Appl. 384(2004), 920. doi:10.1016/j.laa.2003.11.014Google Scholar
[13] Stachó, L. L. and Zalar, B., Bicircular projections and characterization of Hilbert spaces. Proc. Amer. Math. Soc. 132(2004), no. 10, 30193025. doi:10.1090/S0002-9939-04-07333-2Google Scholar