On the ranks of single elements of reflexive operator algebras

William Longstaff, Oreste Panaia

    Research output: Contribution to journalArticle

    13 Citations (Scopus)

    Abstract

    For any completely distributive subspace lattice L on a real or complex reflexive Banach space and a positive integer n, necessary and sufficient (lattice-theoretic) conditions are given for the existence of a single element of AlgL of rank n. Similar conditions are given for the existence of single elements of infinite rank. From this follows a relatively simple lattice-theoretic condition which characterises when every non-zero single element has rank one. Slightly stronger results are obtained for the case where L is finite, including the fact that every single element must then be of finite rank.
    Original languageEnglish
    Pages (from-to)2875-2882
    JournalProceedings of the American Mathematical Society
    Volume125
    Issue number10
    DOIs
    Publication statusPublished - 1997

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