A note on relative amenable of finite von Neumann algebras

2017/05/25 by Xiaoyan Zhou, Zhou, Xiaoyan, Junsheng Fang +1
Mathematics · #46L10 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1705.09018

openalex publication_date 2017/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a finite von Neumann algebra (resp. a type II₁ factor) and let N⊂ M be a II₁ factor (resp. N⊂ M have an atomic part). We prove that the inclusion N⊂ M is amenable implies the identity map on M has an approximate factorization through M_m(ℂ)⊗ N via trace preserving normal unital completely positive maps, which is a generalization of a result of Haagerup. We also prove two permanence properties for amenable inclusions. One is weak Haagerup property, the other is weak exactness.

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