On nearly uniformly convex and k-uniformly convex spaces
Copyright policy )On nearly uniformly convex and k-uniformly convex spaces
AbstractIn 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.
- University of Cambridge United Kingdom
Geometry and structure of normed linear spaces, Isomorphic theory (including renorming) of Banach spaces, fixed-point property for non-expansive mappings, k-uniformly convex spaces, nearly uniformly convex spaces, uniformly Kadec-Klee spaces, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc., normal structure, super-reflexive space, weakly compact convex and bounded set
Geometry and structure of normed linear spaces, Isomorphic theory (including renorming) of Banach spaces, fixed-point property for non-expansive mappings, k-uniformly convex spaces, nearly uniformly convex spaces, uniformly Kadec-Klee spaces, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc., normal structure, super-reflexive space, weakly compact convex and bounded set
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