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

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.

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