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A universal reflexive space for the class of uniformly convex Banach spaces [PDF]

Mathematische Annalen, 2006
We show that there exists a separable reflexive Banach space into which every separable uniformly convex Banach space isomorphically embeds. This solves a problem of J. Bourgain. We also give intrinsic characterizations of separable reflexive Banach spaces which embed into a reflexive space with a block $q$-Hilbertian and/or a block $p$-Besselian ...
E Odell, Th Schlumprecht, Odell E
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Uniformly Strongly Convex Banach Spaces

Mediterranean Journal of Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shunmugaraj, P., Zălinescu, Constantin
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Uniformly smooth renormings of uniformly convex Banach spaces

Journal of Soviet Mathematics, 1985
Translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 135, 120-134 (Russian) (1984; Zbl 0538.46014).
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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 Convex Sets in Banach Spaces

Mathematical Notes
For a normed space \(X\) and for two equivalent asymmetric norms \(\mu_U\), \(\mu_V\) on \(X\) generated by asymmetric unit balls \(U\) and \(V\) respectively, the author introduces and studies the following modulus of convexity of a set \(C \subset X\): \[ \delta_{C,U,V}(\varepsilon)=\inf\left\{\mu_U\left(z-\frac{x+y}{2}\right): x,y \in C, z \in X ...
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Nonexpansive Mappings and Iterative Methods in Uniformly Convex Banach Spaces

gmj, 2002
Abstract In this paper, most of classical and modern convergence theorems of iterative schemes for nonexpansive mappings are presented and the main results in the paper generalize and improve the corresponding results given by many authors.
Zhou, Haiyun, Agarwal, Ravi P., Cho, Yeol Je, Kim, Yong Soo   +3 more
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Farthest points of sets in uniformly convex banach spaces

Israel Journal of Mathematics, 1966
LetS be a closed and bounded set in a uniformly convex Banach spaceX. It is shown that the set of all points inX which have a farthest point inS is dense. Letb(S) denote the set of all farthest points ofS, then a sufficient condition for $$\overline {co} S = \overline {co} b(S)
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Smoothness of the distribution of the norm in uniformly convex Banach spaces

Journal of Theoretical Probability, 1990
Let \((E,\| \cdot \|)\) be a uniformly convex Banach space with modulus of convexity of power type p, F the distribution function of \(\sum^{\infty}_{i=1}\xi_ ix_ i\), where \((x_ i)\) is a sequence of linearly independent elements of E, and \((\xi_ i)\) are independent, real random variables with continuous densities such that \(\sum^{\infty}_{i=1 ...
Byczkowski, Tomasz, Ryznar, Michał
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On embedding trees into uniformly convex Banach spaces

Israel Journal of Mathematics, 1999
The author deals with an investigation into the minimum value of \(D= D(n)\) such that any \(n\)-point tree metric space \((T,\rho)\) can be \(D\)-embedded into a given Banach space \((X,\|\cdot\|)\); i.e., there exists a mapping \(f: T\to X\) such that \(D^{-1}\rho(x,y)\leq\|f(x)- f(y)\|\leq \rho(x,y)\) for all \(x,y\in T\). Bourgain showed that \(X\)
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SIP X_d-frames and their perturbations in uniformly convex Banach spaces

International Journal of Wavelets, Multiresolution and Information Processing, 2014
In this paper, we introduce the definitions of SIP-I and SIP-II Xd-frames in a uniformly convex, separable Banach space X with respect to a BK-space Xd (here SIP represents semi-inner product), both of them are defined as sequence of elements in X.
Xianwei Zheng, Shouzhi Yang
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