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Effros, E.G. and Ruan, Z.-J. (2000) Operator Spaces. In: London Mathematical Society Monographs New Series 23, The Clarendon Press, Oxford University Press, New York.

has been cited by the following article:

• TITLE: The Local Theory of Completely 1-Summing Mapping Spaces

  AUTHORS: Yafei Zhao, Yuanyi Wang

  KEYWORDS: Completely 1-Summing Mapping Space, Injectivity, Nuclearity, Local Reflexivity, Exactness, Finite-Representability and Operator Space

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.6, June 26, 2023

  ABSTRACT: 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 (Ⅱ1(⋅,⋅), π1(⋅)) 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 (Ⅱ1(⋅,⋅), π1(⋅)) if and only if V is finitely representable in {Mn}n∈N in the system (Ⅱ1(⋅,⋅), π1(⋅)). At last, we show that an operator space V is finitely representable in {Mn}n∈N in the system (Ⅱ1(⋅,⋅), π1(⋅)) if and only if V = C.