SEEMINGLY INJECTIVE VON NEUMANN ALGEBRAS  

作　　者：Gilles PISIER 

机构地区：[1]Department of Mathematics,Texas A&M University,College Station,TX,77843-3368,USA

出　　处：《Acta Mathematica Scientia》2021年第6期2055-2085,共31页数学物理学报（B辑英文版）

摘　　要：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 Id_(M)= vu : M→uB(H)→vM 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 I dM through B(H) with u, v positive(and u still normal).

关 键 词：von Neumann algebra INJECTIVITY positive approximation property 

分 类 号：O15[理学—数学]