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 |
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Pages (from-to) | 245-260 |
Journal | Bulletin of the Australian Mathematical Society |
Volume | 58 |
DOIs | |
Publication status | Published - 1998 |