Some strongly bounded classes of Banach spaces [PDF]
arXiv, 2006 We show that the classes of separable reflexive Banach spaces and of spaces with separable dual are strongly bounded. This gives a new proof of a recent result of E. Odell and Th. Schlumprecht, asserting that there exists a separable reflexive Banach space containing isomorphic copies of every separable uniformly convex Banach spaces.
Dodos, Pandelis, Ferenczi, Valentin
arxiv +4 more sources
Separated sequences in uniformly convex Banach spaces [PDF]
Colloq. Math. 102 (2005), 147-153, 2005 We prove that the unit sphere of every infinite-dimensional uniformly convex Banach space with modulus of convexity $\delta$ contains a $(1+\frac12\delta(\frac23))$-separated sequence.
arxiv +6 more sources
Littlewood–Paley inequalities in uniformly convex and uniformly smooth Banach spaces
Journal of Mathematical Analysis and Applications, 2007 Abstract It is proved that the inequality δ X ( e ) ⩾ c e p , p ⩾ 2 , where δ X is the modulus of convexity of X, is sufficient and necessary for the inequality ∫ D ‖ ∇ f ( z ) ‖ p ( 1 − | z | ) p − 1 d A ( z ) ⩽ C ( ‖ f ‖ p , X p − ‖ f ( 0 ) ‖ p ) ,
Karen Avetisyan +2 more
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Fibred cofinitely-coarse embeddability of box families and proper isometric affine actions on uniformly convex Banach spaces [PDF]
arXiv, 2016 In this paper we show that a countable, residually amenable group admits a proper isometric affine action on some uniformly convex Banach space if and only if one (or equivalently, all) of its box families admits a fibred cofinitely-coarse embedding into some uniformly convex Banach space.
Guoqiang Li, Xianjin Wang
arxiv +3 more sources
Mordukhovich derivatives of the metric projection operator in uniformly convex and uniformly smooth Banach spaces [PDF]
arXivIn this paper, we investigate the properties of the Mordukhovich derivatives of the metric projection operator onto closed balls, closed and convex cylinders and positive cones in uniformly convex and uniformly smooth Banach spaces. We find the exact expressions for Mordukhovich derivatives of the metric projection operator.
Jinlu Li
arxiv +2 more sources
The law of the iterated logarithm in uniformly convex Banach spaces [PDF]
Transactions of the American Mathematical Society, 1986 We give necessary and sufficient conditions for a random variable X X with values in a uniformly convex Banach space B B to satisfy the law of the iterated logarithm. Precisely, we show that a B B -valued random variable X X satisfies the (compact) law of the iterated logarithm if ...
Michel Ledoux
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Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces
Journal of Mathematical Analysis and Applications, 1991 AbstractLet X be a real Banach space with dual X∗ and moduli of convexity and smoothness δX(ε) and ϱX(τ), respectively. For 1 < p 0 such that φ(t) ⩾ cδX(t2)} and F= {ϑ: R+ → + : ϑ (0) = 0, ϑ(t) is convex, nondecreasing and there exists K > 0 such that ϑ(τ) ⩽ KϱX(τ)}. It is proved that X is uniformly convex if and only if there is a φ ϵ A such that ∥x +
Zongben Xu, G. F. Roach
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Weak convergence theorems for symmetric generalized hybrid mappings in uniformly convex Banach spaces [PDF]
arXiv, 2014 In this paper, we prove some theorems related to properties of generalized symmetric hybrid mappings in Banach spaces. Using Banach limits, we prove a fixed point theorem for symmetric generalized hybrid mappings in Banach spaces. Moreover, we prove some weak convergence theorems for such mappings by using Ishikawa iteration method in a uniformly ...
Fridoun Moradlou, Sattar Alizadeh
arxiv +3 more sources
Reflexive Banach spaces not isomorphic to uniformly convex spaces [PDF]
Bulletin of the American Mathematical Society, 1941 Mahlon M. Day
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On the Convergence of Some Iteration Processes in Uniformly Convex Banach Spaces [PDF]
Proceedings of the American Mathematical Society, 1978 For the approximation of fixed points of a nonexpansive operator T in a uniformly convex Banach space E the convergence of the Mann-Toeplitz iteration x n + 1 = α n T (
J. Gwinner
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