Nuclearity and Finite-Representability in the System of Completely Integral Mapping Spaces  

作　　者：Zhe DONG Ji Cheng TAO Ya Fei ZHAO 

机构地区：[1]Department of Mathematics,Zhejiang University,Hangzhou 310027,P.R.China [2]Department of Mathematics,China Jiliang University,Hangzhou 310018,P.R.China [3]Department of Mathematics,Zhejiang International Studies University,Hangzhou 310023,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第5期1197-1214,共18页数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11871423);Zhejiang Provincial Natural Science Foundation of China(Grant No.LQ21A010015)。

摘　　要：In this paper,we investigate local properties in the system of completely integral mapping spaces.We introduce notions of injectivity,local reflexivity,exactness,nuclearity,finite-represent ability and WEP in the system of completely integral mapping spaces.First we obtain that any finite-dimensional operator space is injective in the system of completely integral mapping spaces.Furthermore we prove that C is the unique nuclear operator space and the unique exact operator space in this system.We also show that C is the unique operator space which is finitely representable in{T_(n)}n∈Nin this system.As corollaries,Kirchberg’s conjecture and QWEP conjecture in the system of completely integral mapping spaces are false.

关 键 词：Completely integral mapping space injectivity exactness NUCLEARITY finite-representability WEP 

分 类 号：O177[理学—数学]