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Modulus of nearly uniform smoothness and Lindenstrauss formulae

Published online by Cambridge University Press:  18 May 2009

Tomás Domínguez Benavides
Tomás Domínguez Benavides
Affiliation:
Departamento de Ańalisis Matemàtico, Universidad de Sevilla, Apdo.1160, 41080-Sevilla, Spain.
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Abstract

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The Lindenstrauss formula

which states a strong relationship between the (Clarkson) modulus of uniform convexity δx of a Banach space X and the modulus of uniform smoothness px* of the conjugate space X*, is well known. Following the idea of the definitions of nearly uniform smooth space by S. Prus and modulus of uniform smoothness we define a modulus of nearly uniform smoothness and prove some Lindenstrauss type formulae concerning this modulus and the modulus of nearly uniform convexity for some measures of noncompactness.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 37 , Issue 2 , May 1995 , pp. 143 - 153
Copyright
Copyright © Glasgow Mathematical Journal Trust 1995

References

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