Indexed by: Journal Article
Date of Publication: 2019-03-15
Journal: LINEAR ALGEBRA AND ITS APPLICATIONS
Included Journals: EI、SCIE
Volume: 565
Page Number: 239-243
ISSN: 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.