A remark on amenable von Neumann subalgebras in a tracial free product

2015/01/26 by Narutaka Ozawa, Ozawa, Narutaka
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1501.06373

openalex publication_date 2015/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M=M₁*M₂ be a nontrivial tracial free product of finite von Neumann algebras. We prove that any amenable subalgebra of M that has a diffuse intersection with M₁ is in fact contained in M₁. This has been proved by C. Houdayer under more general circumstances.

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