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Stability of weak normal structure in James quasi reflexive space

Published online by Cambridge University Press:  17 April 2009

A. Jiménez-Melado
Affiliation:
Department of Análisis Mathemático, Universidad de Málaga, Facultad de Ciencias 29071 Málaga, Spain
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Abstract

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We introduce a coefficient on general Banach spaces which allows us to derive the weak normal structure for those Banach spaces whose Banach-Mazur distance to James quasi reflexive space is less than .

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Borwein, J.M. and Sims, B., ‘Nonexpansive mappings on Banach lattices and related topics’, Houston J. Math. 10 (1984), 339355.Google Scholar
[2]Gosiez, J.P. and Dozo, E. Lami, ‘Structure normale et base de Schauder’, Bull. Acad. Roy. Belgique 15 (1969), 673681.Google Scholar
[3]Karlovitz, L.A., ‘Existence of fixed points for nonexpansive mappings in a space without normal structure’, Pacific J. Math. 66 (1976), 153159.CrossRefGoogle Scholar
[4]Khamsi, M.A., ‘James quasi reflexive space has the fixed point property’, Bull. Austral. Math. Soc. 39 (1989), 2530.Google Scholar
[5]Khamsi, M.A., ‘Normal structure for Banach spaces with Schauder decomposition’, Canad. Math. Bull. 32 (1989), 344351.Google Scholar
[6]Kirk, W.A., ‘A fixed point theorem for mappings which do not increase distances’, Amer. Math. Monthly 72 (1965), 10041006.CrossRefGoogle Scholar
[7]Lin, P.K., ‘Unconditional bases and fixed points of nonexpansive mappings’, Pacific J. Math. 116 (1985), 6976.CrossRefGoogle Scholar
[8]Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces, Vol I (Springer-Verlag, Berlin, Heidelberg, New York, 1977).CrossRefGoogle Scholar
[9]Maurey, B., ‘Points fixes des contractions sur un convexe ferme de L 1’, in Seminaire d'analyse, fonctionelle (Ecole Polytechnique, Palaiseau, Exposê No. VIII, 1980/1981).Google Scholar
[10]Swaminathan, S., ‘Normal structure in Banach spaces and its generalizations’, Contemp. Math. 18, 201215. A.M.S., Providence, R.I.CrossRefGoogle Scholar
[11]Tingley, D., ‘The normal structure of James quasi reflexive space’, Bull. Austral. Math. Soc. 42 (1990), 95100.CrossRefGoogle Scholar