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Complex uniformly convex Banach spaces and Riesz measures.

Research output: Contribution to journalJournal article

Published

Journal publication date06/2004
JournalCanadian Journal of Mathematics
Journal number2
Volume56
Number of pages21
Pages225-245
Original languageEnglish

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 leq p leq 2.

Bibliographic note

RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics