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A Reflexive LUR Banach Space that Lacks Normal Structure

Published online by Cambridge University Press:  20 November 2018

Mark A. Smith  and
Barry Turett
Mark A. Smith
Affiliation:
Miami University, Oxford, Ohio 45056, U.S.A.
Barry Turett
Affiliation:
Oakland University, Rochester, Michigan 48063, U.S.A.
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Abstract

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An example of the type described in the title is given.

Keywords

46B20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 4 , 01 December 1985 , pp. 492 - 494
Copyright
Copyright © Canadian Mathematical Society 1985

References

1. Belluce, L.P., Kirk, W.A. and Steiner, E.F., Normal structure in Banach spaces, Pac. J. Math. 26 (1968), 433-440.Google Scholar
2. Brodskii, M.S. and Mil'man, D. P., On the center of a convex set, Dokl. Acad. Nauk SSSR (N.S.) 59, (1948), 837-840.Google Scholar
3. Day, M.M., Strict convexity and smoothness of normed spaces, Trans. Amer. Math. Soc. 78 (1955), 516-528.Google Scholar
4. Lovaglia, A.R., Locally uniformly convex Banach spaces, Trans. Amer. Math. Soc. 78 (1955), 225–238.Google Scholar
5. Smith, M.A., Some examples concerning rotundity in Banach spaces, Math. Ann. 233 (1978), 155–161.Google Scholar
6. Swaminathan, S., Normal structure in Banach spaces and its generalizations, in Fixed Points and Nonexpansive Mappings, Contemporary Math. Vol. 18, Amer. Math. Soc, Providence, Rhode Island, 1983, pp. 201–215.Google Scholar