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Locally Uniformly Convex Banach Spaces [PDF]
Transactions of the American Mathematical Society, 1955 which we shall call local uniform convexity. Geometrically this differs from uniform convexity in that it is required that one end point of the variable chord remain fixed. In section I we prove a general theorem on the product of locally uniformly convex Banach spaces and with the aid of this theorem we establish that the two notions are actually ...
A. R. Lovaglia
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Fixed Point Theorems in Uniformly Convex Banach Spaces [PDF]
Proceedings of the American Mathematical Society, 1974 The notion of an asymptotic center is used to prove a number of results concerning the existence of fixed points under certain selfmappings of a closed and bounded convex subset of a uniformly convex Banach space.
Michael Edelstein
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A Generalization of Uniformly Extremely Convex Banach Spaces [PDF]
Journal of Function Spaces, 2016 We discuss a new class of Banach spaces which are the generalization of uniformly extremely convex spaces introduced by Wulede and Ha. We prove that the new class of Banach spaces lies strictly between either the classes ofk-uniformly rotund spaces andk-strongly convex spaces or classes of fullyk-convex spaces andk-strongly convex spaces and has no ...
Suyalatu Wulede +2 more
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Interpolation of uniformly convex Banach spaces [PDF]
Proceedings of the American Mathematical Society, 1982 If A 0 {A_0} and A 1 {A_1} are a compatible couple of Banach spaces, one of which is uniformly convex, then the complex interpolation spaces [ A 0 ,
Michael Ćwikel, Shlomo Reisner
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Bounded cohomology with coefficients in uniformly convex Banach spaces [PDF]
Commentarii Mathematici Helvetici, 2013 We show that for acylindrically hyperbolic groups \Gamma (with no nontrivial finite normal subgroups) and arbitrary unitary representation \rho of \Gamma in a (nonzero) uniformly ...
Mladen Bestvina +2 more
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On set correspondences into uniformly convex Banach spaces [PDF]
Proceedings of the American Mathematical Society, 1972 It is proved that the values of a set-valued set function, the total variation of which is an atomless finite measure, are conditionally convex. Let E be a nonempty o-field of subsets of a set S. A (set) correspondence, say 1, from E to a Banach space X maps, by definition, every element E of E to IF(E), a nonempty subset of X.
David Schmeidler
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Locally uniformly convex norms in Banach spaces and their duals
Journal of Functional Analysis, 2006 It is shown that a Banach space with locally uniformly convex dual admits an equivalent norm which is itself locally uniformly convex. It follows that on any such space all continuous real-valued functions may be uniformly approximated by C^1 functions.
Richard Haydon
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A quantitative Mean Ergodic Theorem for uniformly convex Banach spaces [PDF]
Ergodic Theory and Dynamical Systems, 2008 AbstractWe provide an explicit uniform bound on the local stability of ergodic averages in uniformly convex Banach spaces. Our result can also be viewed as a finitary version in the sense of Tao of the mean ergodic theorem for such spaces and so generalizes similar results obtained for Hilbert spaces by Avigad et al [Local stability of ergodic averages.
Ulrich Kohlenbach, Laurenţiu Leuştean
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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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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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