A class of unitarily invariant norms on $B(H)$
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- by Jor-Ting Chan, Chi-Kwong Li and Charlies C. N. Tu PDF
- Proc. Amer. Math. Soc. 129 (2001), 1065-1076 Request permission
Abstract:
Let $H$ be a complex Hilbert space and let $B(H)$ be the algebra of all bounded linear operators on $H$. For $c=(c_{1},\dots ,c_{k})$, where $c_{1}\ge \cdots \ge c_{k}>0$ and $p\ge 1$, define the $(c,p)$-norm of $A\in B(H)$ by \[ \|A\|_{c,p}=\left (\sum _{i=1}^{k} c_{i} s_{i}(A)^{p}\right )^{\frac {1}{p}} , \] where $s_{i}(A)$ denotes the $i$th $s$-numbers of $A$. In this paper we study some basic properties of this norm and give a characterization of the extreme points of its closed unit ball. Using these results, we obtain a description of the corresponding isometric isomorphisms on $B(H)$.References
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Additional Information
- Jor-Ting Chan
- Affiliation: Department of Mathematics, The University of Hong Kong, Pokfulam, Hong Kong
- Email: jtchan@hkucc.hku.hk
- Chi-Kwong Li
- Affiliation: Department of Mathematics, The College of William & Mary, P.O. Box 8795, Williamsburg, Virginia 23187-8795
- MR Author ID: 214513
- Email: ckli@math.wm.edu
- Charlies C. N. Tu
- Affiliation: Department of Mathematics, The University of Hong Kong, Pokfulam, Hong Kong
- Received by editor(s): June 30, 1999
- Published electronically: October 10, 2000
- Communicated by: David R. Larson
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 1065-1076
- MSC (1991): Primary 47D25
- DOI: https://doi.org/10.1090/S0002-9939-00-05692-6
- MathSciNet review: 1814144