C*-convexity of norm unit balls

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:445

Article

Kian, Mohsen^1,2 

[1] Univ Bojnord, Fac Basic Sci, Dept Math, POB 1339, Bojnord 94531, Iran

[2] Inst Res Fundamental Sci IPM, Sch Math, POB 19395-5746, Tehran, Iran

关键词: C*-convex set;    Unit ball;    Dual norm;   

DOI  :  10.1016/j.jmaa.2016.04.022

来源: Elsevier

【 摘 要 】

We characterize the norms on B(H) whose unit balls are C*-convex. We call such norms M-norms and investigate their dual norms, named L-norms. We show that the class of L-norms greater than a given norm enjoys a minimum element and the class of M-norms less than a given norm enjoys a maximum element. These minimum and maximum elements will be determined in some cases. Finally, we give a constructive result to obtain M-norms and L-norms on B(H). (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free