Unbounded expectations to some von Neumann algebras

Abstract

For any injective von Neumann algebra R and any discrete, countable group G, which acts by *-automorphisms on R, we construct an idempotent mapping of an ultra-weakly dense subspace of B(H) onto the reducerd crossed product von Neumann algebra, such that it is R-bimodular and satisfies some nice relations with respect to positivity. In the case of an amenable group our unbounded expectation turns into a usual conditional expectation of norm 1.

In version 2 the Proposition 3.1 has been improoved and appears as Theorem 3.1. Small changes then follow in the rest

References in corpus (2)

• The Hadamard product in a crossed product C*-algebra
• On a Characterization of the Weak Expectation Property (WEP)