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On nearly uniformly convex Banach spaces

  • J. R. Partington (a1)
Abstract

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.

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(2)A. Brunel and L. Sucheston On B-convex Banach spaces. Math. Systems Theory 7 (1974), 294299.

(3)M. M. Day Some more uniformly convex spaces. Bull. Amer. Math. Soc. 47 (1941), 504507.

(5)R. Huff Banach spaces which are nearly uniformly convex. Rocky Mountain J. Maths. 10 (1980), 743749.

(6)E. Leonard Banach sequence spaces. J. Math. Anal. Appl. 54 (1976), 245265.

(7)E. J. McShane Linear functionals on certain Banach spaces. Proc. Amer. Math. Soc. 1 (1950), 402408.

(10)M. A. Smith and B. Turett Rotundity inLebesgue-Bochner function spaces. Trans. Amer. Math. Soc. 257 (1980), 105118.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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