Indexed by:期刊论文
Date of Publication:2019-03-15
Journal:LINEAR ALGEBRA AND ITS APPLICATIONS
Included Journals:SCIE、EI
Volume:565
Page Number:239-243
ISSN No.:0024-3795
Key Words:Factor von Neumann algebras; Irreducible operators
Abstract:Let M be a factor von Neumann algebra with separable predual and let T is an element of M. We call T an irreducible operator (relative to M) if W*(T) is an irreducible subfactor of M, i.e., W*(T)' boolean AND M = CI. In this note, we show that the set of irreducible operators in M is a dense G(delta) subset of M in the operator norm. This is a natural generalization of a theorem of Halmos. (C) 2018 Elsevier Inc. All rights reserved.