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- W3214472034 endingPage "2085" @default.
- W3214472034 startingPage "2055" @default.
- W3214472034 abstract "We show that a QWEP von Neumann algebra has the weak* positive approximation property if and only if it is seemingly injective in the following sense: there is a factorization of the identity of M $$I{d_M} = vu:Mbuildrel u over longrightarrow B(H)buildrel v over longrightarrow M$$ with u normal, unital, positive and v completely contractive. As a corollary, if M has a separable predual, M is isomorphic (as a Banach space) to B(ℓ2). For instance this applies (rather surprisingly) to the von Neumann algebra of any free group. Nevertheless, since B(H) fails the approximation property (due to Szankowski) there are M’s (namely B(H)** and certain finite examples defined using ultraproducts) that are not seemingly injective. Moreover, for M to be seemingly injective it suffices to have the above factorization of IdM through B(H) with u, v positive (and u still normal)." @default.
- W3214472034 created "2021-11-22" @default.
- W3214472034 creator A5035197493 @default.
- W3214472034 date "2021-11-01" @default.
- W3214472034 modified "2023-09-27" @default.
- W3214472034 title "Seemingly Injective Von Neumann Algebras" @default.
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- W3214472034 doi "https://doi.org/10.1007/s10473-021-0616-0" @default.
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