On irreducible operators in factor von Neumann algebras

2018/05/28 by Junsheng Fang, Rui Shi, Fang, Junsheng +3 · 1 citation
Mathematics · #47C15 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1805.10936

openalex publication_date 2018/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathcal M be a factor von Neumann algebra with separable predual and let T∈ \mathcal M. We call T an irreducible operator (relative to \mathcal M) if W^*(T) is an irreducible subfactor of \mathcal M, i.e., W^*(T)'∩ \mathcal M=\mathbb C I. In this note, we show that the set of irreducible operators in \mathcal M is a dense G_δ subset of \mathcal M in the operator norm. This is a natural generalization of a theorem of Halmos.

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• Products of irreducible operators in factors

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