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Abstract reflexive sublattices and completely distributive collapsibility

  • W. E. Longstaff (a1), J. B. Nation (a1) and Oreste Panaia (a2)

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 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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References

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[11]Panaia, O., Quasi-spatiality of isomorphisms for certain classes of operator algebras, (Ph.D. Thesis) (University of Western Australia, 1995).
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Abstract reflexive sublattices and completely distributive collapsibility

  • W. E. Longstaff (a1), J. B. Nation (a1) and Oreste Panaia (a2)

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