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Abstract reflexive sublattices and completely distributive collapsibility

Published online by Cambridge University Press:  17 April 2009

W. E. Longstaff
Affiliation:
Department of Mathematics, The University of Western Australia, Nedlands, WA 6907, Australia e-mail: longstaf@maths.uwa.edu.au, oreste@maths.uwa.edu.au
J. B. Nation
Affiliation:
Department of Mathematics, The University of Western Australia, Nedlands, WA 6907, Australia e-mail: longstaf@maths.uwa.edu.au, oreste@maths.uwa.edu.au
Oreste Panaia
Affiliation:
Department of Mathematics, University of Hawaii, Honolulu, HI 96822-2273, United States of America e-mail: jb@math.hawaii.edu
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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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1998

References

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