Abstract reflexive sublattices and completely distributive collapsibility

William Longstaff; J.B. Nation; Oreste Panaia

doi:10.1017/S0004972700032226

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 language	English
Pages (from-to)	245-260
Journal	Bulletin of the Australian Mathematical Society
Volume	58
DOIs	https://doi.org/10.1017/S0004972700032226
Publication status	Published - 1998

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title = "Abstract reflexive sublattices and completely distributive collapsibility",

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.",

author = "William Longstaff and J.B. Nation and Oreste Panaia",

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T1 - Abstract reflexive sublattices and completely distributive collapsibility

AU - Longstaff, William

AU - Nation, J.B.

AU - Panaia, Oreste

PY - 1998

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N2 - 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.

AB - 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.

U2 - 10.1017/S0004972700032226

DO - 10.1017/S0004972700032226

M3 - Article

VL - 58

SP - 245

EP - 260

JO - Bulletin of Australian Mathematical Society

JF - Bulletin of Australian Mathematical Society

SN - 0004-9727

ER -