Abstract
If ε>1/4 andX is 3,ε-convex thenX is reflexive. Some additional values ofk and ε with k≧4 are found for whichk,ε-convexity implies reflexivity.
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References
A. Beck,A convexity condition in Banach spaces and the strong law of large numbers, Proc. Amer. Math. Soc.13 (1962), 329–334; see alsoOn the strong law of large numbers, Ergodic Theory, 21–53, Academic Press, New York, 1963.
A. Brunel and L. Sucheston,On B-convex Banach spaces, to appear in Math. Systems Theory.
A. Dvoretzky,some results on convex bodies and Banach spaces, Proceedings of the International Symposium on Linear spaces, 123–160, Pergamon, Press, New York, 1961.
D. P. Giesy,On a convexity condition in normed linear spaces, Trans. Amer. Math. Soc.125 (1966), 114–146; see alsoAdditions and corrections to “On a convexity condition in normed linear spaces”, Trans. Amer. Math. Soc.140 (1969), 511–512.
D. P. Giesy,The completion of a B-convex normed Riesz space is reflexive, J. Functional Analysis12 (1973), 188–198.
D. P. Giesy,Super-reflexivity, stability, and B-convexity, Western Michigan University Mathematics Report 29, August 1972, to appear in Math. Systems Theory.
D. P. Giesy and R. C. James,Uniformly non-l (1) and B-convex spaces, to appear in Studia Math.
R. C. James,Weak compactness and reflexivity, Israel J. Math.2 (1964), 101–119.
R. C. James,Uniformly non-square Banach spaces, Ann. of Math.80 (1964), 542–550.
R. C. James, Lecture Notes, University of Maryland, January, 1972.
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Giesy, D.P. B-convexity and reflexivity. Israel J. Math. 15, 430–436 (1973). https://doi.org/10.1007/BF02757082
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DOI: https://doi.org/10.1007/BF02757082