Projection lattices in a Hilbert space
type: Item
instance of: scholarly article
title: Projection lattices in a Hilbert space
zbMATH Open document ID: 0708.47029
DOI: 10.1007/BF01078796
publication date: 1989-01-01T00:00:00Z
review text: The continuity of the mapping \({\mathcal A}\to Lat {\mathcal A}\) is investigated for subalgebras of a von Neumann algebra. The algebras are supposed closed in the ultraweak topology, Lat \({\mathcal A}\) is identified with the lattices of the corresponding projections. Main result: If lim \({\mathcal A}_ n={\mathcal A}\) then lim Lat \({\mathcal A}_ n=Lat {\mathcal A}\). The limits in the Hausdorff sense, corresponding to the uw topology for the algebras and the strong operator topology for the lattices.
Mathematics Subject Classification ID: 47L30
Mathematics Subject Classification ID: 47A15
Mathematics Subject Classification ID: 46L10
zbMATH DE Number: 4163588
zbMATH Keywords: subalgebras of a von Neumann algebra
zbMATH Keywords: ultraweak topology
zbMATH Keywords: limits in the Hausdorff sense, corresponding to the uw topology for the algebras and the strong operator topology for the lattices
author: V. S. Shulman
reviewed by: Vlastimil Pták
MaRDI profile type: Publication
cites work: On Asymptotically Optimal Hypothesis Testing in Quantum Statistics
cites work: Operator algebras and invariant subspaces
cites work: Tensor products of reflexive subspace lattices
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 4163588