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

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

2004-02-25

arxiv.org/abs/math/0402417v3

Mathematics

Operator Algebras

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

Scientific paper

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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