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    • Nuclearity for Dual Operator Spaces

      Zhe Dong Jicheng Tao

      Volume 120 Issue 1 February 2010 pp 105-111

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/120/01/0105-0111

    • Keywords

       

      Operator space; nuclear; injective.

    • Abstract

       

      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.

    • Author Affiliations

       

      Zhe Dong1 Jicheng Tao2

      1. Department of Mathematics, Zhejiang University, Hangzhou 310 027, China
      2. Department of Mathematics, China Jiliang University, Hangzhou 310 018, China

    • Dates

       
      Published
      February 2010
      Manuscript received
      26 December 2007
      Manuscript revised
      11 November 2009

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