Weak compactness in the dual space of a C*-algebra

C. A. Akemann, P. G. Dodds, J. L.B. Gamlen

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    38 Citations (Scopus)

    Abstract

    Several results in noncommutative measure theory for C*-algebras are proved. A bounded linear map from a C*-algebra to a weakly sequentially complete Banach space is weakly compact (Theorem 4.2). This was a conjecture of Sakai. This result is a consequence of a recent theorem of Pedersen. A theorem of the Vitali-Hahn-Saks type states that a sequence {f{hook}i} of states on a W*-algebra converges weakly if it converges weak* (Corollary 3.3).

    Original languageEnglish
    Pages (from-to)446-450
    Number of pages5
    JournalJournal of Functional Analysis
    Volume10
    Issue number4
    DOIs
    Publication statusPublished - Aug 1972

    Bibliographical note

    Funding Information:
    *Partially supported by NSF grant GP 19101. + Supported in part by NRC grant A 7552.

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