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Lifting of Kadec-Klee Properties to Symmetric Spaces of Measurable Operators
Author(s):
P.
G.
Dodds;
T.
K.
Dodds;
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:
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:
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
Copyright of article:
Copyright
1997,
American Mathematical Society
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