• Nuclearity for Dual Operator Spaces

• # Fulltext

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

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

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019