Abstract reflexive sublattices and completely distributive collapsibility

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.