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

DOI:
https://doi.org/10.1090/S0002-9939-97-03731-3

MathSciNet review:
1371122

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that if is a separable symmetric Banach function space on the positive half-line, then 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 , the associated space of -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:
https://doi.org/10.1090/S0002-9939-97-03731-3

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