Perturbations of von Neumann subalgebras with finite index

2014/07/23 by Shoji Ino, Ino, S.
Mathematics · #46L10 #46L37 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1407.6097

openalex publication_date 2014/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study uniform perturbations of von Neumann subalgebras of a von Neumann algebra. Let N and M be von Neumann subalgebras of a von Neumann algebra with finite probabilistic index in the sense of Pimsner-Popa. If N and M are sufficiently close, then N and M are unitarily equivalent. The implementing unitary can be chosen as being close to the identity.

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