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Complex Uniform Convexity and Riesz Measure

  Published:2004-04-01
 Printed: Apr 2004
  • Gordon Blower
  • Thomas Ransford
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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 $L^p$ 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 $c^p$ are $2$-uniformly $\PL$-convex for $1\leq p\leq 2$.
Keywords: subharmonic functions, Banach spaces, Schatten trace ideals subharmonic functions, Banach spaces, Schatten trace ideals
MSC Classifications: 46B20, 46L52 show english descriptions Geometry and structure of normed linear spaces
Noncommutative function spaces
46B20 - Geometry and structure of normed linear spaces
46L52 - Noncommutative function spaces
 

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