共查询到20条相似文献,搜索用时 0 毫秒
1.
L.Y Nikolova 《Journal of Mathematical Analysis and Applications》2003,283(2):549-556
We show how uniform convexity can be preserved in the logarithmic spaces Aθ(logA)b,p. Estimates are given for the moduli of convexity of Aθ(logA)b,p in terms of the moduli of A0 and A1, when one or both of them are uniformly convex. 相似文献
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R. Bruce Richter 《Discrete Mathematics》2011,(15):1390
Thomassen and Vella (Graph-like continua, augmenting arcs, and Menger’s Theorem, Combinatorica, doi:10.1007/s00493-008-2342-9) have recently introduced the notion of a graph-like space, simultaneously generalizing infinite graphs and many of the compact spaces recently used by Diestel or Richter (and their coauthors) to study cycle spaces and related problems in infinite graphs. This work is a survey to introduce graph-like spaces and shows how many of these works on compact spaces can be generalized to compact graph-like spaces. 相似文献
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Wen Zhang 《数学学报(英文版)》2012,28(7):1369-1374
By a ball-covering B of a Banach space X, wemean that B is a collection of open (or closed) balls off the origin whose union contains the unit sphere of X; and X is said to have the ball-covering property provided it admits a ball-covering of countably many balls. This paper shows that universal finite representability and B-convexity of X can be characterized by properties of ball-coverings of its finite dimensional subspaces. 相似文献
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We pursue the study of the multiscale spaces Sν introduced by Jaffard in the context of multifractal analysis. We give the necessary and sufficient condition for Sν to be locally p-convex, and exhibit a sequence of p-norms that defines its natural topology. The strong topological dual of Sν is identified to another sequence space depending on ν, endowed with an inductive limit topology. As a particular case, we describe the dual of a countable intersection of Besov spaces. 相似文献
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该文利用Hahn Banach定理得到了凸性模定义中若干等式的证明,并且指出对维数不小
于2的实线性赋范空间犡,有类似的等式成立。 相似文献
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An upper bound q(c) for the best, under equivalent renorming, possible power type of the modulus of smoothness of a Banach space with modulus of convexity satisfying δX(ε)?cε2, is found. The estimate is asymptotically sharp and is expressed in terms of linear fractional function q(c). 相似文献
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We introduce a few functions related to convexity and smoothness of normed spaces. Those functions turn out to be moduli of
convexity or smoothness or play an intermediate role. We calculate the exact formulas for introduced functions in some classical
Banach spaces. An application to geometry of normed spaces is also indicated. 相似文献
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Let X be a Banach space with closed unit ball B. Given k
, X is said to be k-β, respectively, (k + 1)-nearly uniformly convex ((k + 1)-NUC), if for every ε > 0 there exists δ, 0 < δ < 1, so that for every x B and every ε-separated sequence (xn) B there are indices (ni)ki = 1, respectively, (ni)k + 1i = 1, such that (1/(k + 1))||x + ∑ki = 1 xni|| ≤ 1 − δ, respectively, (1/(k + 1))||∑k + 1i = 1 xni|| ≤ 1 − δ. It is shown that a Banach space constructed by Schachermayer is 2-β, but is not isomorphic to any 2-NUC Banach space. Modifying this example, we also show that there is a 2-NUC Banach space which cannot be equivalently renormed to be 1-β. 相似文献
10.
Ji Gao 《Journal of Mathematical Analysis and Applications》2007,334(1):114-122
Let X be a normed linear space and be the unit sphere of X. Let , , and J(X)=sup{‖x+y‖∧‖x−y‖}, x and y∈S(X) be the modulus of convexity, the modulus of smoothness, and the modulus of squareness of X, respectively. Let . In this paper we proved some sufficient conditions on δ(?), ρX(?), J(X), E(X), and , where the supremum is taken over all the weakly null sequence xn in X and all the elements x of X for the uniform normal structure. 相似文献
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A short introduction of Hamilton, Cartan and Generalized Hamilton spaces is provided. The Hamilton--Jacobi equations are deduced by variational calculus. 相似文献
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Let denote the space of all holomorphic functions on the unit ball . This paper investigates the following integral-type operator with symbol where is the radial derivative of g. The boundedness and compactness of the operator Tg from Bloch-type spaces to Zygmund-type spaces are studied. 相似文献
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The boundedness and compactness of the products of differentiation and composition operators from Zygmund spaces to Bloch spaces and Bers spaces are discussed in this paper. 相似文献
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Eva Matousková Charles Stegall 《Proceedings of the American Mathematical Society》1996,124(4):1083-1090
A Banach space is not reflexive if and only if there exist a closed separable subspace of and a convex closed subset of with empty interior which contains translates of all compact sets in . If, moreover, is separable, then it is possible to put .
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We prove the following theorem: in Hilbert space a closed bounded set is contained in the strongly convex R-hull of its R-strong extreme points. R-strong extreme points are a subset of the set of extreme points (it may happen that these two sets do not coincide); the strongly convex R-hull of a set contains the closure of the convex hull of the set. 相似文献
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Several fixed point theorems for symmetric spaces are proved. Then these theorems are used in symmetric PPM-space to prove and generalize Theorem 6 of [T.L. Hicks, B.E. Rhoades, Fixed point theory in symmetric spaces with applications to probabilistic spaces, Nonlinear Anal. 36 (1999) 331-344]. 相似文献
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Sarason has shown that the local Dirichlet spaces Dλ may be considered as manifestations of de Branges-Rovnyak spaces H(b), and has used this identification to give a new proof that the spaces Dλ are star-shaped. We investigate which other Dirichlet spaces D(μ) arise as de Branges-Rovnyak spaces, and which other de Branges-Rovnyak spaces H(b) are star-shaped. We also prove a transfer principle which represents H(b)-spaces inside Dλ. 相似文献
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IMRE Z. Ruzsa 《Geometriae Dedicata》1997,67(3):337-348
We improve the Brunn–Minkowski inequality for nonconvex sets. Besides the volume of the sets, our estimate depends on the volume of the convex hull of one of the sets. The estimate is asymptotically the best possible if this set is fixed and the size of the other tends to infinity. 相似文献
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Javier Alonso Enrique Llorens-Fuster 《Journal of Mathematical Analysis and Applications》2008,340(2):1271-1283
We consider the triangles with vertices x, −x and y where x,y are points on the unit sphere of a normed space. Using the geometric means of the variable lengths of the sides of these triangles, we define two geometric constants for Banach spaces. These constants are closely related to the modulus of convexity of the space under consideration, and they seem to represent a useful tool to estimate the exact values of the James and Jordan–von Neumann constants of some Banach spaces. 相似文献