Weak limits of projections and compactness of subspace lattices

Weak Limits of Projections and Compactness of Subspace Lattices

A strongly closed lattice of projections on a Hubert space is compact if the associated algebra of operators has a weakly dense subset of compact operators. If the lattice is commutative, there are necessary and sufficient conditions for compactness, one in terms of the structure of the lattice, and the other in terms of a measure on the lattice. There are many examples of compact lattices, and...

Weak Compactness of the Set of ε-Extensions

On compactness of lattices

In this paper, we present a study of various concepts pertaining to compactness properties of a lattice. Special cases include such notions as countably compactness, almost countably compactness, and countably paracompactness. Some investigations in these matters have been done in [2, 7, 14]. We go beyond these results and introduce new subsets of I(L) and their lattices to investigate. This wa...

On compactness and projections

Convergence, Closed Projections and Compactness

In this paper several results of N. Noble concerning closed projections are extended using generalizations of first countable, Frechet, and sequential spaces. We also consider compactness conditions defined by requiring that certain nets have cluster points.