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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Lifting of Kadec-Klee Properties
to Symmetric Spaces of Measurable Operators


Authors: P. G. Dodds, T. K. Dodds and F. A. Sukochev
Journal: Proc. Amer. Math. Soc. 125 (1997), 1457-1467
MSC (1991): Primary 46L50, 46E30; Secondary 46B20, 47D15
MathSciNet review: 1371122
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that if $E$ is a separable symmetric Banach function space on the positive half-line, then $E$ has the Kadec-Klee property (respectively, uniform Kadec-Klee property) for local convergence in measure if and only if, for every semifinite von Neumann algebra $( \mathcal {M}, \tau )$, the associated space $ E(\mathcal {M},\tau )$ of $\tau $-measurable operators has the same property.


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Additional Information

P. G. Dodds
Affiliation: Department of Mathematics and Statistics, Flinders University, GPO Box 2100, Adelaide, SA 5001, Australia
Email: peter@ist.flinders.edu.au

T. K. Dodds
Affiliation: Department of Mathematics and Statistics, Flinders University, GPO Box 2100, Adelaide, SA 5001, Australia
Email: theresa@ist.flinders.edu.au

F. A. Sukochev
Affiliation: Department of Mathematics and Statistics, Flinders University, GPO Box 2100, Adelaide, SA 5001, Australia
Email: sukochev@ist.flinders.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03731-3
PII: S 0002-9939(97)03731-3
Keywords: Kadec-Klee properties, rearrangement-invariant spaces, measurable operators, submajorization
Received by editor(s): June 2, 1995
Received by editor(s) in revised form: November 27, 1995
Additional Notes: Research supported by A.R.C
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society