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Characterizations of Kadec-Klee properties in symmetric spaces of measurable functions


Authors: V. I. Chilin, P. G. Dodds, A. A. Sedaev and F. A. Sukochev
Journal: Trans. Amer. Math. Soc. 348 (1996), 4895-4918
MSC (1991): Primary 46E30; Secondary 46B20, 46B42
DOI: https://doi.org/10.1090/S0002-9947-96-01782-5
MathSciNet review: 1390973
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Abstract: We present several characterizations of Kadec-Klee properties in symmetric function spaces on the half-line, based on the $K$-functional of J. Peetre. In addition to the usual Kadec-Klee property, we study those symmetric spaces for which sequential convergence in measure (respectively, local convergence in measure) on the unit sphere coincides with norm convergence.


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Additional Information

V. I. Chilin
Affiliation: Department of Mathematics, Tashkent State University, Tashkent 700095, Uzbekistan

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

A. A. Sedaev
Affiliation: Department of Mathematics, Voronež Civil Engineering Institute, Voronež, 394000, Russia

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

DOI: https://doi.org/10.1090/S0002-9947-96-01782-5
Keywords: Symmetric spaces, Kadec-Klee properties, Lorentz spaces
Received by editor(s): October 29, 1994
Received by editor(s) in revised form: May 25, 1995
Additional Notes: Research of the second and fourth authors was supported by the Australian Research Council.
Article copyright: © Copyright 1996 American Mathematical Society

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