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Reflexivity of the group of surjective isometries on some Banach spaces

Published online by Cambridge University Press:  20 January 2009

Lajos Molnár  and
Borut Zalar
Lajos Molnár
Affiliation:
Institute of Mathematics, Lajos Kossuth University, 4010 Debrecen, P.O. Box 12, Hungary, E-mail address: molnarl@math.klte.hu
Borut Zalar
Affiliation:
Department of Basic Sciences, Faculty of Civil Engineering, University of mariborSmetanova 17 62000 MariborSlovenija E-mail address: borut.zalar@uni-mb.si or borut.zalar@uni-lj.si
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In this paper we study the problem of algebraic reflexivity of the isometry group of some important Banach spaces. Because of the previous work in similar topics, our main interest lies in the von Neumann – Schatten p-classes of compact operators. The ideas developed there can be used in ℓp-spaces, Banach spaces of continuous functions and spin factors as well. Moreover, we attempt to attract the attention to this problem from general Banach spaces geometry view-point. This study, we believe, would provide nice geometrical results.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 42 , Issue 1 , February 1999 , pp. 17 - 36
Copyright
Copyright © Edinburgh Mathematical Society 1999

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