Compactness and Complete Distributivity for Commutative Subspace Lattices
Kenneth R. Davidson, David R. Pitts · Journal of the London Mathematical Society · 1990
In this note, we show that if L is a commutative subspace lattice generated by a completely distributive lattice and finitely many commuting chains, then L is compact in the strong operator topology if and only if L is completely distributive. The key device used is a new characterization of complete distributivity which we call upper (or lower) semicontinuity.