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 syst...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.展开更多
In this paper, we investigate local properties in the system of completely 1-summing mapping spaces. We introduce notions of injectivity, local reflexivity, exactness, nuclearity and finite-representability in the sys...In this paper, we investigate local properties in the system of completely 1-summing mapping spaces. We introduce notions of injectivity, local reflexivity, exactness, nuclearity and finite-representability in the system of completely 1-summing mapping spaces. First we obtain that if V has WEP, V is locally reflexive in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if it is locally reflexive in the system (Ⅰ(⋅,⋅), t(⋅)). Furthermore we prove that an operator space V ⊆ B(H) is exact in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if V is finitely representable in {M<sub>n</sub>}<sub>n∈N</sub> in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)). At last, we show that an operator space V is finitely representable in {M<sub>n</sub>}<sub>n∈N</sub> in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if V = C.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11871423)Zhejiang Provincial Natural Science Foundation of China(Grant No.LQ21A010015)。
文摘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.
文摘In this paper, we investigate local properties in the system of completely 1-summing mapping spaces. We introduce notions of injectivity, local reflexivity, exactness, nuclearity and finite-representability in the system of completely 1-summing mapping spaces. First we obtain that if V has WEP, V is locally reflexive in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if it is locally reflexive in the system (Ⅰ(⋅,⋅), t(⋅)). Furthermore we prove that an operator space V ⊆ B(H) is exact in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if V is finitely representable in {M<sub>n</sub>}<sub>n∈N</sub> in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)). At last, we show that an operator space V is finitely representable in {M<sub>n</sub>}<sub>n∈N</sub> in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if V = C.
