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Abstract reflexive sublattices and completely distributive collapsibility
Published online by Cambridge University Press: 17 April 2009
Abstract
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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 δ on ℒ such that ℒ/δ is completely distributive is well-behaved. Our results are purely lattice theoretic, but the motivation comes from operator theory.
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- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 58 , Issue 2 , October 1998 , pp. 245 - 260
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- Copyright © Australian Mathematical Society 1998
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