Complex Uniform Convexity and Riesz Measures

Blower, Gordon ; Ransford, Thomas

Canadian journal of mathematics, Tome 56 (2004) no. 2, pp. 225-245

Résumé

The norm on a Banach space gives rise to a subharmonic function on the complex plane for which the distributional Laplacian gives a Riesz measure. This measure is calculated explicitly here for Lebesgue ${{L}^{p}}$ spaces and the von Neumann-Schatten trace ideals. Banach spaces that are $q$ -uniformly $\text{PL}$ -convex in the sense of Davis, Garling and Tomczak-Jaegermann are characterized in terms of the mass distribution of this measure. This gives a new proof that the trace ideals ${{c}^{p}}$ are 2-uniformly $\text{PL}$ -convex for $1\,\le \,p\,\le \,2$ .

Détail

DOI : 10.4153/CJM-2004-011-3

Mots-clés : 46B20, 46L52, subharmonic functions, Banach spaces, Schatten trace ideals

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