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 syst...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.展开更多
基金National Natural Science Foundation of China (Grant No. 11871423)。
文摘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.
