共查询到20条相似文献,搜索用时 46 毫秒
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A net (xα) in a vector lattice X is said to be unbounded order convergent (or uo-convergent, for short) to x∈X if the net (|xα−x|∧y) converges to 0 in order for all y∈X+. In this paper, we study unbounded order convergence in dual spaces of Banach lattices. Let X be a Banach lattice. We prove that every norm bounded uo-convergent net in X? is w?-convergent iff X has order continuous norm, and that every w?-convergent net in X? is uo-convergent iff X is atomic with order continuous norm. We also characterize among σ -order complete Banach lattices the spaces in whose dual space every simultaneously uo- and w?-convergent sequence converges weakly/in norm. 相似文献
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Let X be a reflexive Banach space which does not have the Kadec–Klee property. Then there exists a compact mapping f from the unit ball BX of X to the dual space X? such that infx∈BX‖f(x)‖>0 and 〈f(x),x〉<‖f(x)‖ for every x∈BX. 相似文献
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In this paper, we give a new proof of a result of R. Jones showing almost everywhere convergence of spherical means of actions of Rd on Lp(X)-spaces are convergent for d?3 and p>d/(d-1). 相似文献
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Jean-Pierre Kahane 《Comptes Rendus Mathematique》2014,352(5):383-385
For almost all x>1, (xn)(n=1,2,…) is equidistributed modulo 1, a classical result. What can be said on the exceptional set? It has Hausdorff dimension one. Much more: given an (bn) in [0,1[ and ε>0, the x -set such that |xn−bn|<ε modulo 1 for n large enough has dimension 1. However, its intersection with an interval [1,X] has a dimension <1, depending on ε and X. Some results are given and a question is proposed. 相似文献
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A weak selection on an infinite set X is a function σ:[X]2→X such that σ({x,y})∈{x,y} for each {x,y}∈[X]2. A weak selection on a space is said to be continuous if it is a continuous function with respect to the Vietoris topology on [X]2 and the topology on X . We study some topological consequences from the existence of a continuous weak selection on the product X×Y for the following particular cases:
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- Both X and Y are spaces with one non-isolated point. 相似文献
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In this paper, we introduce the metric dG on a G -metric space (X,G) and use this notion to show that many contraction conditions for maps on the G -metric space (X,G) reduce to certain contraction conditions for maps on the metric space (X,dG). As applications, the proofs of many fixed point theorems for maps on the G -metric space (X,G) may be simplified, and many fixed point theorems for maps on the G -metric space (X,G) are direct consequences of preceding results for maps on the metric space (X,dG). 相似文献
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This paper treats some variational principles for solutions of inhomogeneous p -Laplacian boundary value problems on exterior regions U?RN with dimension N?3. Existence-uniqueness results when p∈(1,N) are provided in a space E1,p(U) of functions that contains W1,p(U). Functions in E1,p(U) are required to decay at infinity in a measure theoretic sense. Various properties of this space are derived, including results about equivalent norms, traces and an Lp-imbedding theorem. Also an existence result for a general variational problem of this type is obtained. 相似文献
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Let (X,L) be a polarized Kähler manifold that admits an extremal metric in c1(L). We show that on a nearby polarized deformation (X′,L′) that preserves the symmetry induced by the extremal vector field of (X,L), the modified K-energy is bounded from below. This generalizes a result of Chen, Székelyhidi and Tosatti , and to extremal metrics. Our proof also extends a convexity inequality on the space of Kähler potentials due to X.X. Chen [7] to the extremal metric setup. As an application, we compute explicit polarized 4-points blow-ups of CP1×CP1 that carry no extremal metric but with modified K-energy bounded from below. 相似文献
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