On subspace lattices I. Closedness type properties and tensor products

V.S. Shulman; Ivan Todorov

doi:10.1007/s00020-002-1291-8

On subspace lattices I. Closedness type properties and tensor products

V.S. Shulman, Ivan Todorov

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	561-579
Number of pages	19
Journal	Integral Equations and Operator Theory
Volume	52
Issue number	4
DOIs	https://doi.org/10.1007/s00020-002-1291-8
Publication status	Published - Aug 2005

ASJC Scopus subject areas

Algebra and Number Theory
Analysis

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10.1007/s00020-002-1291-8

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abstract = "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.",

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AB - 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.

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SN - 0378-620X

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On subspace lattices I. Closedness type properties and tensor products

Abstract

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