On the Relative Weak Asymptotic Homomorphism Property for Triples of Groups von Neumann Algebras

Abstract

We provide a direct and elementary proof of the equivalence between the weak asymptotic homomorphism property for the pair of group von Neumann algebras $L(H)\subset L(G)$ and the embedding into $H$ of the one sided quasi-normalizer of the pair $H<G$, as it is stated by J. Fang, M. Gao and R. R. Smith in a recent article, and we extend the result to triples of groups $H<K<G$.

One more condition added; it is expressed in terms of compact vectors

References in corpus (1)

• On the normalizing algebra of a MASA in a II${}_1$ Factor