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Normal structure coefficients of Lp(Ω)

Published online by Cambridge University Press:  14 November 2011

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

Let X be a uniformly convex Banach space, and N(X) the normal structure coefficient of X. In this paper it is proved that N(X) can be calculated by considering only sets whose points are equidistant from their Chebyshev centre. This result is applied to prove that N(LP(Ω)) = min {21−1/p, 21/p}, Ω being a σ-finite measure space. The computation of N(Lp) lets us also calculate some other coefficients related to the normal structure.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 117 , Issue 3-4 , 1991 , pp. 299 - 303
Copyright
Copyright © Royal Society of Edinburgh 1991

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