论文标题
看似注入式冯·诺伊曼代数
Seemingly injective von Neumann algebras
论文作者
论文摘要
我们表明，QWEP von Neumann代数具有弱*正近似属性，并且仅当它看似以下意义上是注入的：$ m $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ = vu：m {\ buildrel u \ y \ longrightArlow} b（h）b（h）b（h）b（h）{正面和$ v $完全承包。作为推论，如果$ m $具有可分离的预性，则$ m $是同构（作为Banach空间）至$ b（\ ell_2）$。例如，这（令人惊讶的是）适用于任何自由组的von Neumann代数。然而，由于$ b（h）$未能使近似属性（由于szankowski）失败，因此有$ m $（即$ b（h）^{**} $，而某些使用Ultraproducts定义的有限示例似乎并不注射。此外，对于$ m $，似乎是注入式的，就可以将上述分解为$ id_m $ ta $ b（h）$，而$ u，v $ atention（和$ u $仍然很正常）。
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 $M$ $$Id_M=vu: M{\buildrel u\over\longrightarrow} B(H) {\buildrel v\over\longrightarrow} M$$ 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 $B(\ell_2)$. 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 $Id_M$ through $B(H)$ with $u,v$ positive (and $u$ still normal).
