On the Notion of Relative Property (T) for Inclusions of Von Neumann Algebras

2004/02/25 by Jesse Peterson, Peterson, Jesse, Sorin Popa +1
Mathematics · #22D10 #22D25 #46L10 #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Operator Algebras (math.OA) #Rings, Modules, and Algebras #math.OA #msc:22D10 #msc:22D25 #msc:46L10

paper · pdf · doi:10.48550/arxiv.math/0402417

12 pages; additions on 03/17/04, 15 pages

openalex publication_date 2004/02/25 · arxiv created 2004/03/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the notion of relative property (T) (or rigidity) for inclusions of finite von Neumann algebras defined in [Po1] is equivalent to a weaker property, in which no ``continuity constants'' are required. The proof is by contradiction and uses infinite products of completely positive maps, regarded as correspondences.

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