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Complex Uniform Convexity and Riesz Measures

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>1/04/2004
<mark>Journal</mark>Canadian Journal of Mathematics
Issue number2
Volume56
Number of pages21
Pages (from-to)225-245
Publication StatusPublished
<mark>Original language</mark>English

Abstract

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 Lp spaces and the von Neumann-Schatten trace ideals. Banach spaces that are q -uniformly 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 cp are 2-uniformly PL -convex for 1≤p≤2 .