A note on characterizations of relative amenability on finite von Neumann algebras

2018/07/05 by Xiaoyan Zhou, Zhou, Xiaoyan, Junsheng Fang +1
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1807.01905

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

Abstract

In this paper, we give another two characterizations of relative amenability on finite von Neumann algebras, one of which can be thought of as an analogue of injective operator systems. As an application, we prove a stable property of relative amenable inclusions. We prove that under certain assumptions, the inclusion N=∫_X \bigoplus N_p d μ⊂ M=∫_X \bigoplus M_p d μ is amenable if and only if N_p⊂ M_p is amenable almost everywhere.

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