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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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References

1Amir, D.. On Jung's constant and related constants in normed linear spaces. Pacific J. Math. 118 (1985), 1–15.CrossRefGoogle Scholar
2Ayerbe, J. M. and Benavides, T. Dominguez. Set-contractions and ball-contractions in L p-spaces J. Math. Anal. Appl. (to appear).Google Scholar
3Bynum, W. L.. Normal structure coefficients for Banach spaces. Pacific J. Math. 86 (1980), 427–435.Google Scholar
4Casini, E. and Maluta, E.. Fixed points of uniformly Lipschitzian mappings in spaces with uniformly normal structure. Nonlinear Anal. 9 (1985), 103–108.CrossRefGoogle Scholar
5Lim, T. C.. On the normal structure coefficient and the bounded sequence coefficient. Proc. Amer. Math. Soc. 88 (1983), 262–264.Google Scholar
6Lim, T. C.. Some L P inequalities and their applications to fixed point theorems of uniformly Lipschitzian mappings. Proc. Sympos. Pure Math. 45 (1986), Pt. 2, 119–125.Google Scholar
7Maluta, E.. Uniformly normal structure and related coefficients. Pacific J. Math. 111 (1984), 357–369.CrossRefGoogle Scholar
8Webb, J. R. L. and Zhao, W.. Connections between set and ball measures of noncompactness (Preprint series, Paper No. 89/56, Department of Mathematics, University of Glasgow, 1989).Google Scholar
9Wells, J. H. and Williams, L. R.. Embeddings and Extensions in Analysis (Berlin: Springer 1975).CrossRefGoogle Scholar
10Xu, H. and Xu, Z.. An L P inequality and its applications to fixed point theory and approximation theory. Proc. Roy. Soc. Edinburgh Sect. A 112 (1989), 343–351.CrossRefGoogle Scholar