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Journal of Convex Analysis 18 (2011), No. 1, 059--065
Copyright Heldermann Verlag 2011

A Representation of G-invariant norms for Eaton Triple

Piotr Niemiec
Jagiellonian University, Institute of Mathematics, ul. Lojasiewicza 6, 30-348 Kraków, Poland

Tin-Yau Tam
Dept. of Mathematics and Statistics, Auburn University, Auburn, AL 36849-5310, U.S.A.

We obtain a representation of unitarily invariant norm in terms of Ky Fan norms [see R. Bhatia, Matrix Analysis, Springer, New York et al., 1997, p. 35]. Indeed we obtain a more general result in the context of Eaton triple with reduced triple. Examples are given.

Keywords: Eaton triple, G-invariant norms, symmetric gauge functions, Ky Fan norms, finite reflection groups.

MSC: 15A60, 65F35

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