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Normal Structure for Banach Spaces with Schauder Decomposition

Published online by Cambridge University Press:  20 November 2018

M. A. Khamsi*
Affiliation:
Department of Mathematics University of Southern California Los Angeles, CA.
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Abstract

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We introduce a new constant in Banach spaces which implies, in certain cases, the weak- or weak*-normal structure.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Andrew, A., Spreading basic sequences and subspaces of James quasi reflexive space.Math. Scad. 48 (1981), 108118.Google Scholar
2. Beauzamy, B. and Lapreste, J. T., Modèles étalés des espaces de Banach, Publication du Dept. de Math. Université Claude Barnard-Lyon 1.Google Scholar
3. Brodskii, M. S. and D. P. Mil'man, On the center of a convex set, Dokl. Akad. Nauk, USSR 59 (1948) 837840.Google Scholar
4. Brunei, A. and Sucheston, L., On B-convex Banach spaces, Math. System Theory, 7 (1974) 294299.Google Scholar
5. Bynum, W. L., Normal structure coefficients for Banach spaces, Pac. J. Math. Vol. 86, No. 2, (1980) 427436.Google Scholar
6. Day, M. M., Normed linear spaces, 3rd Edn. Springer-Verlag, 1973.Google Scholar
7. Guerre, S. and J. T. Lapreste, Quelques propriétés des modèles étalés sur un espace de Banach, Ann. IHP. Section B 16-4 (1980) 339347.Google Scholar
8. James, R. C., Bases and reflexivity of Banach spaces, Ann. of Math. 52 (1950) 518527.Google Scholar
9. Khamsi, M. A., James quasi-reflexive space has the fixed point property, to appear in Bull. Aust. Math. Soc.Google Scholar
10. Kirk, W. A., A fixed point theorem for mappings which do not increase distance, Amer. Math. Monthly 72 (1965) 1004-1006. MR 32=6436.Google Scholar
11. Kirk, W. A., Fixed point theory for non expansive mappings, II. Contemporary Mathematics, Vol. 18 (1983) 121140.Google Scholar
12. Landes, T., Permanence properties of normal structure, Pac. J. Math. Vol 110, No. 1 (1984) 125— 143.Google Scholar
13. Lim, T. C., Asymptotic centers and nonexpansive mappings in conjugate Banach spaces, Pac. J. Math. 90 (1980) 134143.Google Scholar
14. Lindenstrauss, J. and Tzafriri, L., Classical Banach Spaces-I-Sequence spaces, Springer-Verlag 1977.Google Scholar
15. Sims, B., “Ultra“-techniques in Banach space theory, Queen's papers in Pure and Applied Mathematics, no. 60, Queen's University, Kingston, Ontario, Canada.Google Scholar
16. Soardi, P. M., Schauder bases and fixed points of nonexpansive mappings, Pac. J. Math. Vol. 101, No. 1 (1982) 193198.Google Scholar
17. Swaminathan, S., Normal structure in Banach spaces and its generalizations, Contemporary Mathematics, Vol. 18 (1983) 201215.Google Scholar