Kirchberg’s conjecture in the system of Hilbert space factorable mapping spaces  

作　　者：Zhe Dong 

机构地区：[1]School of Mathematical Sciences,Zhejiang University,Hangzhou 310027,China

出　　处：《Science China Mathematics》2020年第6期1125-1138,共14页中国科学：数学（英文版）

基　　金：National Natural Science Foundation of China (Grant No. 11871423)。

摘　　要：This study aims to introduce the notions of injectivity, local reflexivity, exactness, and nuclearity in the system(Γ2c(·, ·), γ2c(·)). We find that every dual operator space is injective in the system(Γ2c(·, ·), γ2c(·)) and nuclearity is equivalent to exactness in this system. As a corollary, we prove that Kirchberg’s conjecture on the equivalence of exactness and local reflexivity for C*-algebras is false in this system, i.e., there exists a C*-algebra A that is locally reflexive in this system but is not exact in this system.

关 键 词：Hilbert space factorable mapping space INJECTIVITY local reflexivity EXACTNESS NUCLEARITY 

分 类 号：O177.1[理学—数学]