• Zhe Dong

      Articles written in Proceedings – Mathematical Sciences

    • Nuclearity for Dual Operator Spaces

      Zhe Dong Jicheng Tao

      More Details Abstract Fulltext PDF

      In this short paper, we study the nuclearity for the dual operator space $V^∗$ of an operator space 𝑉. We show that $V^∗$ is nuclear if and only if $V^{∗∗∗}$ is injective, where $V^{∗∗∗}$ is the third dual of 𝑉. This is in striking contrast to the situation for general operator spaces. This result is used to prove that $V^{∗∗}$ is nuclear if and only if 𝑉 is nuclear and $V^{∗∗}$ is exact.

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