Search results for "Dual space"

Complete weights andv-peak points of spaces of weighted holomorphic functions

2006

We examine the geometric theory of the weighted spaces of holomorphic functions on bounded open subsets ofC n ,C n ,H v (U) and\(H_{v_o } (U)\), by finding a lower bound for the set of weak*-exposed and weak*-strongly exposed points of the unit ball of\(H_{v_o } (U)'\) and give necessary and sufficient conditions for this set to be naturally homeomorphic toU. We apply these results to examine smoothness and strict convexity of\(H_{v_o } (U)\) and\(H_v (U)\). We also investigate whether\(H_{v_o } (U)\) is a dual space.

General duality in vector optimization

1993

Vector minimization of a relation F valued in an ordered vector space under a constraint A consists in finding x 0 ∊ A w,0 ∊ Fx$0 such that w,0 is minimal in FA. To a family of vector minimization problemsminimize , one associates a Lagrange relation where ξ belongs to an arbitrary class Ξ of mappings, the main purpose being to recover solutions of the original problem from the vector minimization of the Lagrange relation for an appropriate ξ. This ξ turns out to be a solution of a dual vector maximization problem. Characterizations of exact and approximate duality in terms of vector (generalized with respect to Ξ) convexity and subdifferentiability are given. They extend the theory existin…

On the stability of the Bohl — Brouwer — Schauder Theorem

1996

(p,q)-summing sequences

2002

Abstract A sequence (x j ) in a Banach space X is (p,q) -summing if for any weakly q -summable sequence (x j ∗ ) in the dual space we get a p -summable sequence of scalars (x j ∗ (x j )) . We consider the spaces formed by these sequences, relating them to the theory of (p,q) -summing operators. We give a characterization of the case p=1 in terms of integral operators, and show how these spaces are relevant for a general question on Banach spaces and their duals, in connection with Grothendieck theorem.

A note on the closed graph theorem

1977

Partitions of finite vector spaces: An application of the frobenius number in geometry

1978

Wolfe's theorem for weakly differentiable cochains

2014

Abstract A fundamental theorem of Wolfe isometrically identifies the space of flat differential forms of dimension m in R n with the space of flat m -cochains, that is, the dual space of flat chains of dimension m in R n . The main purpose of the present paper is to generalize Wolfe's theorem to the setting of Sobolev differential forms and Sobolev cochains in R n . A suitable theory of Sobolev cochains has recently been initiated by the second and third author. It is based on the concept of upper norm and upper gradient of a cochain, introduced in analogy with Heinonen–Koskela's concept of upper gradient of a function.

Lacunary Bifurcation of Multiple Solutions of Nonlinear Eigenvalue Problems

1991

In order to describe the type of nonlinear eigenvalue problems we are going to discuss, consider a densely defined closed linear operator T in a real Hilbert space H and let H1 be the Hilbert space which consists of the domain of T together with the graph norm. Also, let H 1 * be the dual space of H1 and denote the dual operator corresponding to T: H1 → H by T’:H → H 1 * . Since H1 is dense in H, we may view H as a subspace of H1, and then the scalar product (·,·) on H and the dual pairing on H1 × H 1 * coincide on H1 × H.

Characterizations of convex approximate subdifferential calculus in Banach spaces

2016

International audience; We establish subdifferential calculus rules for the sum of convex functions defined on normed spaces. This is achieved by means of a condition relying on the continuity behaviour of the inf-convolution of their corresponding conjugates, with respect to any given topology intermediate between the norm and the weak* topologies on the dual space. Such a condition turns out to also be necessary in Banach spaces. These results extend both the classical formulas by Hiriart-Urruty and Phelps and by Thibault.