The Experts below are selected from a list of 6576 Experts worldwide ranked by ideXlab platform
Yuuji Tanaka - One of the best experts on this subject based on the ideXlab platform.
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a Weak Compactness theorem of the donaldson thomas instantons on compact kahler threefolds
Journal of Mathematical Analysis and Applications, 2013Co-Authors: Yuuji TanakaAbstract:In Tanaka [18], we introduced a gauge-theoretic equation on symplectic 6-manifolds, which is a version of the Hermitian–Einstein equation perturbed by Higgs fields, and called it a Donaldson–Thomas equation, to analytically approach the Donaldson–Thomas invariants. In this article, we consider the equation on compact Kahler threefolds, and study some of the analytic properties of solutions to them, using analytic methods in higher-dimensional Yang–Mills theory developed by Nakajima (1987) [14], Nakajima (1988) [15] and Tian (2000) [20] with some additional arguments concerning an extra nonlinear term coming from the Higgs fields. We prove that a sequence of solutions to the Donaldson–Thomas equation of a unitary vector bundle over a compact Kahler threefold has a converging subsequence outside a closed subset whose real two-dimensional Hausdorff measure is finite, provided that the L2-norms of the Higgs fields are uniformly bounded. We also prove an n/2-Compactness theorem of solutions to the equations on compact Kahler threefolds.
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a Weak Compactness theorem of the donaldson thomas instantons on compact k ahler threefolds
arXiv: Differential Geometry, 2008Co-Authors: Yuuji TanakaAbstract:In arXiv:0805.2192, we set up a gauge-theoretic equation on symplectic 6-manifolds, which is a version of the Hermitian-Einstein equation perturbed by Higgs fields, and call Donaldson-Thomas equation, to analytically approach the Donaldson-Thomas invariants. In this article, we consider the equation on compact K\"ahler threefolds, and study some of analytic properties of solutions to them, using analytic methods in higher-dimensional Yang-Mills theory developed by Nakajima and Tian with some additional arguments concerning an extra non-linear term coming from the Higgs fields. We prove that a sequence of solutions to the Donaldson-Thomas equation of a unitary vector bundle over a compact K\"ahler threefold has a converging subsequence outside a closed subset whose real 2-dimensional Hausdorff measure is finite, provided that the L^2-norms of the Higgs fields are uniformly bounded. We also prove an n/2-Compactness theorem of solutions to the equations on compact K\"ahler threefolds.
Hermann Pfitzner - One of the best experts on this subject based on the ideXlab platform.
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boundaries for banach spaces determine Weak Compactness
Inventiones Mathematicae, 2010Co-Authors: Hermann PfitznerAbstract:A boundary for a real Banach space is a subset of the dual unit sphere with the property that each element of the Banach space attains its norm on an element of that subset. Trivially, the pointwise convergence with respect to such a boundary is coarser than the Weak topology on the Banach space. The boundary problem asks whether nevertheless both topologies have the same norm bounded compact sets.
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boundaries for banach spaces determine Weak Compactness
arXiv: Functional Analysis, 2008Co-Authors: Hermann PfitznerAbstract:A boundary for a Banach space is a subset of the dual unit sphere with the property that each element of the Banach space attains its norm on an element of that subset. Trivially, the pointwise convergence with respect to such a boundary is coarser than the Weak topology on the Banach space. Godefroy's Boundary Problem asks whether nevertheless both topologies have the same bounded compact sets. This paper contains the answer in the positive.
J Vielma - One of the best experts on this subject based on the ideXlab platform.
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Weak sequential convergence and Weak Compactness in spaces of vector valued continuous functions
Journal of Mathematical Analysis and Applications, 1995Co-Authors: Surjit Singh Khurana, J VielmaAbstract:Abstract Let X be completely regular Hausdorff space, E a Hausdorff locally convex space, C(X, E) (Cb(X, E)) the space of all E-valued (all E-valued bounded) continuous functions on X, and βz a strict topology on Cb(X, E). It is proved that a sequence {ƒn} in (Cb(X, E), βz) converges Weakly to 0 if and only if {ƒn} is uniformly bounded and ƒn,(x) → 0, pointwise on X with Weak topology on E. Similar results are proved for (C(X, E), β∞c). Some characterizations of relatively Weakly compact subsets of (Cb(X, E), βz) and (C(X, E), β∞c) are also given.
Jichao Zhang - One of the best experts on this subject based on the ideXlab platform.
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on super fixed point property and super Weak Compactness of convex subsets in banach spaces
Journal of Mathematical Analysis and Applications, 2015Co-Authors: Lixin Cheng, Qingjin Cheng, Jichao ZhangAbstract:Abstract For a nonempty convex set C of a Banach space X, a self-mapping on C is said to a linear (respectively, affine) isometry if it is the restriction of a linear (respectively, affine) isometry defined on the whole space X. By means of super Weakly compact set theory established in the recent years, in this paper, we first show that a nonempty closed bounded convex set of a Banach space has super fixed point property for affine (or, equivalently, linear) isometries if and only if it is super Weakly compact; and the super fixed point property and the super Weak Compactness coincide on every closed bounded convex subset of a Banach space under equivalent renorming sense. With the application of Fabian–Montesinos–Zizler's renorming theorem, we finally show that every strongly super Weakly compact generated Banach space can be renormed so that every Weakly compact convex set has super fixed point property.
Surjit Singh Khurana - One of the best experts on this subject based on the ideXlab platform.
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Weakly compact sets in L∞(μ,E)
Journal of Functional Analysis, 2012Co-Authors: Surjit Singh KhuranaAbstract:Abstract Using the theory of liftings, we give simple new proofs of the characterizations of the relatively Weakly compact subsets and Weak Cauchy sequences of L ∞ ( E ) . Also a different proof, of a deep result of J. Diestel, W. Ruess, W. Schachermayer about Weak Compactness in L 1 ( E ) , is given.
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Weak sequential convergence and Weak Compactness in spaces of vector valued continuous functions
Journal of Mathematical Analysis and Applications, 1995Co-Authors: Surjit Singh Khurana, J VielmaAbstract:Abstract Let X be completely regular Hausdorff space, E a Hausdorff locally convex space, C(X, E) (Cb(X, E)) the space of all E-valued (all E-valued bounded) continuous functions on X, and βz a strict topology on Cb(X, E). It is proved that a sequence {ƒn} in (Cb(X, E), βz) converges Weakly to 0 if and only if {ƒn} is uniformly bounded and ƒn,(x) → 0, pointwise on X with Weak topology on E. Similar results are proved for (C(X, E), β∞c). Some characterizations of relatively Weakly compact subsets of (Cb(X, E), βz) and (C(X, E), β∞c) are also given.
