Blower, Gordon and Ransford, T. J.
(2004)
*Complex uniformly convex Banach spaces and Riesz measures.*
Canadian Journal of Mathematics, 56 (2).
pp. 225-245.
ISSN 0008-414X

## 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.

Item Type:

Journal Article

Journal or Publication Title:

Canadian Journal of Mathematics

Additional Information:

RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics

Uncontrolled Keywords:

/dk/atira/pure/researchoutput/libraryofcongress/qa

Subjects:

?? SUBHARMONIC FUNCTIONSBANACH SPACESSCHATTEN TRACE IDEALSMATHEMATICS(ALL)QA MATHEMATICS ??

Departments:

ID Code:

2368

Deposited By:

Deposited On:

01 Apr 2008 14:20

Refereed?:

Yes

Published?:

Published

Last Modified:

21 Sep 2023 00:44