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- W2151900546 abstract "A triple of finite von Neumann algebras B ⊆ N ⊆ M is said to have the relative weak asymptotic homomorphism property if there exists a net of unitary operators {u λ } λ∈Λ in B such that [Formula: see text] for all x,y ∈ M. We prove that a triple of finite von Neumann algebras B ⊆ N ⊆ M has the relative weak asymptotic homomorphism property if and only if N contains the set of all x ∈ M such that [Formula: see text] for a finite number of elements x 1 , …, x n in M. Such an x is called a one-sided quasi-normalizer of B, and the von Neumann algebra generated by all one-sided quasi-normalizers of B is called the one-sided quasi-normalizer algebra of B. We characterize one-sided quasi-normalizer algebras for inclusions of group von Neumann algebras and use this to show that one-sided quasi-normalizer algebras and quasi-normalizer algebras are not equal in general. We also give some applications to inclusions L(H) ⊆ L(G) arising from containments of groups. For example, when L(H) is a masa we determine the unitary normalizer algebra as the von Neumann algebra generated by the normalizers of H in G." @default.
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- W2151900546 date "2011-07-01" @default.
- W2151900546 modified "2023-10-01" @default.
- W2151900546 title "THE RELATIVE WEAK ASYMPTOTIC HOMOMORPHISM PROPERTY FOR INCLUSIONS OF FINITE VON NEUMANN ALGEBRAS" @default.
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- W2151900546 doi "https://doi.org/10.1142/s0129167x11007203" @default.
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