Lifting of kadec-klee properties to symmetric spaces of measurable operators

P. G. Dodds, T. K. Dodds, F. A. Sukochev

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

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 (M,τ), the associated space E(M, τ) of τ-measurable operators has the same property.

Original languageEnglish
Pages (from-to)1457-1467
Number of pages11
JournalProceedings of the American Mathematical Society
Volume125
Issue number5
DOIs
Publication statusPublished - May 1997

Keywords

  • Kadec-klee properties
  • Measurable operators, submajorization
  • Rearrangement-invariant spaces

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