Results 1 to 10 of about 476,682 (147)
Locally uniformly convex norms in Banach spaces and their duals [PDF]
arXiv, 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
arxiv +7 more sources
A quantitative Mean Ergodic Theorem for uniformly convex Banach spaces [PDF]
arXiv, 2008 We 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 T. Tao of the Mean Ergodic Theorem for such spaces and so generalizes similar results obtained for Hilbert spaces by Avigad, Gerhardy and Towsner (arXiv:0706.1512v2 [math ...
Ulrich Kohlenbach, Laurenţiu Leuştean
arxiv +7 more sources
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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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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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
openalex +3 more sources
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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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
openalex +3 more sources
Directional Differentiability of the Metric Projection in Uniformly Convex and Uniformly Smooth Banach Spaces [PDF]
arXiv, 2023 Let X be a real uniformly convex and uniformly smooth Banach space and C a nonempty closed and convex subset of X. Let Pc from X to C denote the (standard) metric projection operator. In this paper, we define the Gateaux directional differentiability of Pc. We investigate some properties of the Gateaux directional differentiability of Pc. In particular,
Li, Jinlu
arxiv +2 more sources
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
openalex +3 more sources
Remarks on quasi-isometric non-embeddability into uniformly convex Banach spaces [PDF]
arXiv, 2005 We construct a locally finite graph and a bounded geometry metric space which do not admit a quasi-isometric embedding into any uniformly convex Banach space. Connections with the geometry of $c_0$ and superreflexivity are discussed.
Piotr W. Nowak
arxiv +3 more sources