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Weak compactness criteria in symmetric spaces of measurable operators

Published online by Cambridge University Press:  26 October 2001

P. G. DODDS ,
F. A. SUKOCHEV  and
G. SCHLÜCHTERMANN
P. G. DODDS
Affiliation:
Department of Mathematics and Statistics, The Flinders University of South Australia, GPO Box 2100, Adelaide, SA 5001, Australia. e-mail: peter@ist.flinders.edu.au, sukochev@ist.flinders.edu.au
F. A. SUKOCHEV
Affiliation:
Department of Mathematics and Statistics, The Flinders University of South Australia, GPO Box 2100, Adelaide, SA 5001, Australia. e-mail: peter@ist.flinders.edu.au, sukochev@ist.flinders.edu.au
G. SCHLÜCHTERMANN
Affiliation:
Mathematisches Institut, der Universität München, Theresienstraße 39, D-80333, München, Germany. e-mail: schluech@rz.mathematik.uni-muenchen.de
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Abstract

The principal result of the paper reduces the study of certain weakly compact sets in Banach spaces of measurable operators to that of the corresponding sets of generalized singular value functions. In particular, under natural conditions, it is shown that the orbit of a relatively weakly compact subset of the Köthe dual of a symmetric space of measurable operators affiliated with some semi-finite von Neumann algebra is again relatively weakly compact.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 131 , Issue 2 , September 2001 , pp. 363 - 384
Copyright
2001 Cambridge Philosophical Society

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