Characterizations of kadec-klee properties in symmetric spaces of measurable functions

V. I. Chilin, P. G. Dodds, A. A. Sedaev, F. A. Sukochev

Research output: Contribution to journalArticlepeer-review

39 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)4895-4918
Number of pages24
JournalTRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume348
Issue number12
DOIs
Publication statusPublished - Dec 1996

Keywords

  • Kadec-klee properties
  • Lorentz spaces
  • Symmetric spaces

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