We study properties of subspace lattices related to the continuity of the map Lat and the notion of reflexivity. We characterize various “closedness” properties in different ways and give the hierarchy between them. We investigate several properties related to tensor products of subspace lattices and show that the tensor product of the projection lattices of two von Neumann algebras, one of which is injective, is reflexive.
ASJC Scopus subject areas
- Algebra and Number Theory
Shulman, V. S., & Todorov, I. (2005). On subspace lattices I. Closedness type properties and tensor products. Integral Equations and Operator Theory, 52(4), 561-579. https://doi.org/10.1007/s00020-002-1291-8