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On nearly uniformly convex and k-uniformly convex spaces
Published online by Cambridge University Press: 24 October 2008
Abstract
In this note we prove that every nearly uniformly convex space has normal structure and that K-uniformly convex spaces are super-reflexive.
We recall [1] that a Banach space is said to be Kadec–Klee if whenever xn → x weakly and ∥n∥ = ∥x∥ = 1 for all n then ∥xn −x∥ → 0. The stronger notions of nearly uniformly convex spaces and uniformly Kadec–Klee spaces were introduced by R. Huff in [1]. For the reader's convenience we recall them here.
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- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 95 , Issue 2 , March 1984 , pp. 325 - 327
- Copyright
- Copyright © Cambridge Philosophical Society 1984
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