超积、QWEP von Neumann Algebras和Effros-Maréchal拓扑
Ultraproducts, QWEP von Neumann Algebras, and the Effros-Maréchal Topology
摘要：
通过对作用在可分希尔伯特空间H上的von Neumann代数的Ocneanu/Groh-Raynaud超积和空间vN（H）上的Effros-Maréchal拓扑的分析，证明了对于vN（H）中的von Neumann代数M，下列条件是等价的：（1）M具有Kirhcberg商弱期望性质（QWEP）. (2)M是H上内射因子集F_{inj}关于Effros-Maréchal拓扑的闭包。(3)M允许将i嵌入到单射III_1因子R_{\infty}的Ocneanu超幂R_{infty} ^{omega}中，具有正常的忠实条件期望R_{infty} ^{omega}到i（M）。(4)对于每个n>0，自然数n和xi_1，.，xi_n在P_M^{natural}中，存在自然数k和a_1，.，a_nin M_k（C）_+，使得|<xi_i，xi_j>-tr_k（a_ia_j）|其中tr_k是M_k（C）上的迹态，P_M^{natural}是M的标准式的自然锥.
英文摘要：
Based on the analysis on the Ocneanu/Groh-Raynaud ultraproducts and the Effros-Maréchal topology on the space vN(H) of von Neumann algebras acting on a separable Hilbert space H, we show that for a von Neumann algebra M in vN(H), the following conditions are equivalent: (1) M has the Kirhcberg's quotient weak expectation property (QWEP). (2) M is in the closure of the set F_{inj of injective factors on H with respect to the Effros-Maréchal topology. (3) M admits an embedding i into the Ocneanu ultrapower R_{infty}^{omega} of the injective III_1 factor R_{\infty} with a normal faithful conditional expectation epsilon: R_{infty}^{omega} to i(M). (4) For every epsilon>0, natural number n, and xi_1,...,xi_n in P_M^{natural}, there is a natural number k and a_1,...,a_nin M_k(C)_+, such that |<xi_i,xi_j>-tr_k(a_ia_j)|<epsilon (1<=i,j<=n) holds, where tr_k is the tracial state on M_k(C), and P_M^{natural} is the natural cone in the standard form of M.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
