Complex Uniform Convexity and Riesz Measures

Blower, G. and Ransford, T. (2004) Complex Uniform Convexity and Riesz Measures. Canadian Journal of Mathematics, 56 (2). pp. 225-245. ISSN 0008-414X

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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 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 .

Item Type:
Journal Article
Journal or Publication Title:
Canadian Journal of Mathematics
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600
Subjects:
ID Code:
149283
Deposited By:
Deposited On:
23 Nov 2020 12:25
Refereed?:
Yes
Published?:
Published
Last Modified:
25 May 2021 07:59