数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (6): 1981-1988.doi: 10.1007/s10473-020-0623-6

• 论文 • 上一篇    下一篇

ON THE NUCLEARITY OF COMPLETELY 1-SUMMING MAPPING SPACES

董浙1, 赵亚菲2   

  1. 1. School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China;
    2. Department of Mathematics, Zhejiang International Studies University, Hangzhou 310012, China
  • 收稿日期:2019-04-06 修回日期:2020-07-24 出版日期:2020-12-25 发布日期:2020-12-30
  • 作者简介:Zhe DONG,E-mail:dongzhe@zju.edu.cn;Yafei ZHAO,E-mail:zhaoyafei_zju@163.com
  • 基金资助:
    The project was partially supported by the National Natural Science Foundation of China (11871423).

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).

摘要: 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.

关键词: λ-nuclearity, completely 1-summing mapping space

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

中图分类号: 

  • 46B07