Properties (u) and (V*) of Pelczynski in symmetric spaces of T-measurable operators

Peter Dodds, Bernardus De Pagter

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    It is shown that order continuity of the norm and weak sequential completeness in non-commutative strongly symmetric spaces of τ-measurable operators are respectively equivalent to properties (u) and (V*) of Pelczynski. In addition, it is shown that each strongly symmetric space with separable (Banach) bidual is necessarily reflexive. These results are non-commutative analogues of well-known characterisations in the setting of Banach lattices.

    Original languageEnglish
    Pages (from-to)571-594
    Number of pages24
    JournalPositivity
    Volume15
    Issue number4
    DOIs
    Publication statusPublished - 2011

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