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- Title
Nuclearity and Finite-Representability in the System of Completely Integral Mapping Spaces.
- Authors
Dong, Zhe; Tao, Ji Cheng; Zhao, Ya Fei
- Abstract
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-representability 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 {Tn}n∈ℕ in this system. As corollaries, Kirchberg's conjecture and QWEP conjecture in the system of completely integral mapping spaces are false.
- Subjects
INTEGRALS; INJECTIVE functions; REFLEXIVITY
- Publication
Acta Mathematica Sinica, 2024, Vol 40, Issue 5, p1197
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-023-2103-0