Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

A class of unitarily invariant norms on

Author(s): Jor-Ting Chan; Chi-Kwong Li; Charlies C. N. Tu
Journal: Proc. Amer. Math. Soc. 129 (2001), 1065-1076.
MSC (1991): Primary 47D25
Posted: October 10, 2000
MathSciNet review: 1814144
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Abstract | References | Similar articles | Additional information

Abstract: Let be a complex Hilbert space and let be the algebra of all bounded linear operators on . For $c=(c_{1},\dots ,c_{k})$ , where $c_{1}\ge \cdots \ge c_{k}>0$ and $p\ge 1$ , define the -norm of $A\in B(H)$ by

$\begin{displaymath}\Vert A\Vert _{c,p}=\left (\sum _{i=1}^{k} c_{i} s_{i}(A)^{p}\right )^{\frac{1}{p}} , \end{displaymath}$

where $s_{i}(A)$ denotes the

-numbers of

. 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

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