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Lower bounds for normal structure coefficients

Published online by Cambridge University Press:  14 November 2011

T. Domínguez Benavides  and
G. López Acedo
T. Domínguez Benavides
Affiliation:
Departamento de Análisis Matemático Facultad de Matemáticas, Universidad de Sevilla, Apart. 1160, 41080 Sevilla, Spain
G. López Acedo
Affiliation:
Departamento de Análisis Matemático Facultad de Matemáticas, Universidad de Sevilla, Apart. 1160, 41080 Sevilla, Spain
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Synopsis

Using some new expressions for the weakly convergent sequences coefficient WCS(X) the lower boundedness

is proved, where δ(-) is the (Clarkson) modulus of convexity. We also define a modulus of noncompact convexity concerning nearly uniformly convex spaces which is used to obtain another lower bound for WCS(X). The computation of this modulus in Ip-spaces shows that our second lower bound is the best possible in these spaces.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 121 , Issue 3-4 , 1992 , pp. 245 - 252
Copyright
Copyright © Royal Society of Edinburgh 1992

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