Sequential convergence in the order duals of certain classes of riesz spaces

P. G. Dodds

    Research output: Contribution to journalArticlepeer-review

    12 Citations (Scopus)

    Abstract

    Several results of Hahn-Vitali-Saks type are given for sequences in the order dual of an Archimedean Riesz space with separating order dual. The class of Riesz spaces considered contains those which are Dedekind ocomplete, or have the projection property or have an interpolation property introduced by G. L. Seever. The results depend on recent work of O. Burkinshaw and some results of uniform boundedness type.

    Original languageEnglish
    Pages (from-to)391-403
    Number of pages13
    JournalTRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
    Volume203
    DOIs
    Publication statusPublished - 1975

    Keywords

    • Archimedean Riesz spaces
    • Order dual
    • Principal projection property
    • Sequential convergence
    • Weak compactness

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