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The normal structure of James quasi reflexive space

Published online by Cambridge University Press:  17 April 2009

Daryl Tingley
Daryl Tingley
Affiliation:
Department of Mathematics and Statistics, University of New Brunswick Predericton, N. B., Canada, E3B 5A3
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Abstract

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It is shown that weakly compact sets of James quasi reflexive space have normal structure.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 42 , Issue 1 , August 1990 , pp. 95 - 100
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Borwein, J.M. and Sims, B., ‘Nonexpansive mappings on Banach lattices and related topics’, Houston J. Math. 10 (1984), 339–355.Google Scholar
[2]Brodskii, M.S. and Milman, D.P., ‘On the center of a convex set’, Dokl. Akad. Nauk SSSR 59 (1948), 837–840.Google Scholar
[3]James, R.C., ‘A non-reflexive Banach space isometric with its second conjugate space’, Proc. Nat. Acad. Sci. U.S.A. 37 (1951), 134–177.CrossRefGoogle ScholarPubMed
[4]Karlovitz, L.A., ‘Existence of fixed points for nonexpansive mappings in a space without normal structure’, Pacific J. Math. 66 (1976), 153–159.CrossRefGoogle Scholar
[5]Kirk, W.A., ‘A fixed point theorem for mappings, which do not increase distances’, Amer. Math. Monthly 72 (1965), 1004–1006.CrossRefGoogle Scholar
[6]Khamsi, M.A., ‘Normal structure for Banach spaces with Schauder decomposition’, Canadian Math. Bull. 32 (1989), ??–??.CrossRefGoogle Scholar
[7]Khamsi, M.A., ‘James quasi reflexive space has the fixed point property’, Bull. Austral. Math. Soc. 39 (1989), 25–30.CrossRefGoogle Scholar
[8]Lin, P.K., ‘Unconditional bases and fixed points of nonexpansive mappings’, Pacific J. Math. 116 (1985), 69–76.CrossRefGoogle Scholar
[9]Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces, Vol. I and II (Springer-Verlag, Berlin, Heidelberg, New York, 1977 and 1979).CrossRefGoogle Scholar
[10]Maurey, B., Points fixes des contractions sur un convexe ferme de L1: Seminaire d'analyse fonctionelle (Ecole Polytechnique, Palaiseau, Exposé No. VIII, 1980/81).Google Scholar
[11]Swaminathan, S., ‘Normal structure in Banach spaces and its generalization’, Contemp. Math. 18, 201–215. (A.M.S., Providence, R.I.).CrossRefGoogle Scholar