Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (6): 1981-1988.doi: 10.1007/s10473-020-0623-6

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ON THE NUCLEARITY OF COMPLETELY 1-SUMMING MAPPING SPACES

Zhe DONG1, Yafei ZHAO2   

  1. 1. School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China;
    2. Department of Mathematics, Zhejiang International Studies University, Hangzhou 310012, China
  • Received:2019-04-06 Revised:2020-07-24 Online:2020-12-25 Published:2020-12-30
  • Supported by:
    The project was partially supported by the National Natural Science Foundation of China (11871423).

Abstract: In this paper, we investigate the $\lambda$-nuclearity in the system of completely 1-summing mapping spaces $(\Pi_{1}(\cdot, \cdot), \pi_{1})$. In Section 2, we obtain that $\mathbb{C}$ is the unique operator space that is nuclear in the system $(\Pi_{1}(\cdot, \cdot), \pi_{1})$. We generalize some results in Section 2 to $\lambda$-nuclearity in Section 3.

Key words: λ-nuclearity, completely 1-summing mapping space

CLC Number: 

  • 46B07
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