Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Complex uniformly convex Banach spaces and Riesz measures.
AU - Blower, Gordon
AU - Ransford, T. J.
N1 - RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics
PY - 2004/6
Y1 - 2004/6
N2 - 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.
AB - 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.
KW - subharmonic functions
KW - Banach spaces
KW - Schatten trace ideals
M3 - Journal article
VL - 56
SP - 225
EP - 245
JO - Canadian Journal of Mathematics
JF - Canadian Journal of Mathematics
SN - 0008-414X
IS - 2
ER -