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On nearly uniformly convex Banach spaces

Published online by Cambridge University Press:  24 October 2008

J. R. Partington
J. R. Partington
Affiliation:
Pembroke College, Cambridge
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Extract

A real Banach space (X, ‖ · ‖) is said to be uniformly convex (UC) (or uniformly rotund) if for all ∈ > 0 there is a δ > 0 such that if ‖x| ≤ 1, ‖y‖ ≤ 1 and ‖x−y‖ ≥ ∈, then ‖(x + y)/2‖ ≤ 1− δ.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 93 , Issue 1 , January 1983 , pp. 127 - 129
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

REFERENCES

(1)Baernstein, A. IIOn reflexivity and summability. Studia. Math. 42 (1972), 91–94.CrossRefGoogle Scholar
(2)Brunel, A. and Sucheston, L.On B-convex Banach spaces. Math. Systems Theory 7 (1974), 294–299.CrossRefGoogle Scholar
(3)Day, M. M.Some more uniformly convex spaces. Bull. Amer. Math. Soc. 47 (1941), 504–507.CrossRefGoogle Scholar
(4)Day, M. M.Normed linear spaces, 3rd ed. (Springer, 1972.)Google Scholar
(5)Huff, R.Banach spaces which are nearly uniformly convex. Rocky Mountain J. Maths. 10 (1980), 743–749.Google Scholar
(6)Leonard, E.Banach sequence spaces. J. Math. Anal. Appl. 54 (1976), 245–265.CrossRefGoogle Scholar
(7)McShane, E. J.Linear functionals on certain Banach spaces. Proc. Amer. Math. Soc. 1 (1950), 402–408.CrossRefGoogle Scholar
(8)Partington, J. R.On the Banach-Saks property. Math. Proc. Cambridge Philos. Soc. 82 (1977), 369–374.CrossRefGoogle Scholar
(9)Seifert, C. J.The dual of Baernstein's space and the Banach-Saks property. Bull. Acad. Pol. Sci. (Ser. Sci. Math. Astr. et Phys.) 26 (1978), 237–239.Google Scholar
(10)Smith, M. A. and Turett, B.Rotundity inLebesgue-Bochner function spaces. Trans. Amer. Math. Soc. 257 (1980), 105–118.CrossRefGoogle Scholar