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Uniformly convex Banach spaces are reflexive—constructively [PDF]

open access: possibleMathematical Logic Quarterly, 2013
We propose a natural definition of what it means in a constructive context for a Banach space to be reflexive, and then prove a constructive counterpart of the Milman‐Pettis theorem that uniformly convex Banach spaces are reflexive.
Douglas S. Bridges   +2 more
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BASES IN UNIFORMLY CONVEX AND UNIFORMLY FLATTENED BANACH SPACES

Mathematics of the USSR-Izvestiya, 1971
The aim of this article is to obtain two-sided estimates for the norm of an element x in a uniformly convex and uniformly flattened Banach space E in terms of lp-norms of the sequence of coefficients which occur in the expansion of x in a basis .
V I Gurariĭ, N I Gurariĭ
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On nearly uniformly convex Banach spaces

Mathematical Proceedings of the Cambridge Philosophical Society, 1983
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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Uniformly smooth renormings of uniformly convex Banach spaces

Journal of Soviet Mathematics, 1985
In this note we study the quantitative side of the famous Enflo-Pisier theorem on the possibility of equivalent uniformly smooth renormings of superreflexive Banach spaces (in particular, uniformly convex and uniformly nonsquare ones). Typical re result: let the modulus of convexity of the space X, which has a locally unconditional structure, satisfy ...
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Smoothness of the distribution of the norm in uniformly convex Banach spaces

Journal of Theoretical Probability, 1990
Let (E, ‖ · ‖) be a uniformly convex Banach space of power type. In this paper we investigate differentiability properties of the distribution function of the norm of a random series with one-dimensional independent components inE.
Michał Ryznar, Tomasz Byczkowski
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