Abstract reflexive sublattices and completely distributive collapsibility

William Longstaff, J.B. Nation, Oreste Panaia

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    19 Citations (Scopus)

    Abstract

    There is a natural Galois connection between subspace lattices and operator algebras on a Banach space which arises from the notion of invariance. If a subspace lattice L is completely distributive, then L is reflexive. In this paper we study the more general situation of complete lattices for which the least complete congruence Delta on L such that L/Delta is completely distributive is well-behaved. Our results are purely lattice theoretic, but the motivation comes from operator theory.
    Original languageEnglish
    Pages (from-to)245-260
    JournalBulletin of the Australian Mathematical Society
    Volume58
    DOIs
    Publication statusPublished - 1998

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