Results 1 to 10 of about 10,923 (164)

On Weak Compactness in $L_1$ Spaces

Rocky Mountain Journal of Mathematics, 2009
The Banach space \(Z\) is said to strongly generate the Banach space \(X\) if there exists a \(T\in L(Z,X)\) such that, for every weakly compact set \(W\subset X\) and every \(\varepsilon>0\), there is a natural number \(m\) such that \(W\subset mT(B_Z)+\varepsilon B_X\).
Vicente Montesinos
exaly   +5 more sources

Weak Compactness in W^k,∞

Mathematics
We characterize weak compactness in the Sobolev space Wk,∞(Ω). For non-reflexive spaces like Wk,∞, criteria beyond boundedness are required. By exploiting the von Neumann algebra structure of L∞ via Gelfand duality, we establish a unified theory.
Cheng Chen, Shiqing Zhang
doaj   +2 more sources

On invex programming problem in Hilbert spaces [PDF]

Yugoslav Journal of Operations Research, 2015
In this paper we introduce the invex programming problem in Hilbert space. The requisite theory has been established to characterize the solution of such class of problems.
Chatterjee Sandip, Mukherjee Rathindranath   +1 more
doaj   +1 more source

Smoothness and Weak Sequential Compactness [PDF]

Proceedings of the American Mathematical Society, 1980
If a Banach space E has an equivalent smooth norm, then every bounded sequence in E ∗ {E^\ast } has a weak ∗ {\text {weak}^\ast } converging subsequence. Generalizations of this result are obtained.
Hagler, James, Sullivan, Francis
openaire   +1 more source

Convergence of Weak*-Scalarly Integrable Functions

Axioms, 2020
Let (Ω,F,μ) be a complete probability space, E a separable Banach space and E′ the topological dual vector space of E. We present some compactness results in LE′1E, the Banach space of weak*-scalarly integrable E′-valued functions.
Noureddine Sabiri, Mohamed Guessous
doaj   +1 more source

On the Strength of Weak Compactness [PDF]

Computability, 2012
We study the logical and computational strength of weak compactness in the separable Hilbert space ℓ2. Let weak-BW be the statement the every bounded sequence in ℓ2 has a weak cluster point. It is known that weak-BW is equivalent to ACA0 over RCA0 and thus that it is equivalent to (nested uses of) the usual Bolzano-Weierstraß principle BW. We show that
openaire   +2 more sources

Weak Compactness and Vector Measures [PDF]

Canadian Journal of Mathematics, 1955
Introduction. It is the purpose of this paper to develop a Lebesgue theory of integration of scalar functions with respect to a countably additive measure whose values lie in a Banach space. The class of integrable functions reduces to the ordinary space of Lebesgue integrable functions if the measure is scalar valued.
Bartle, R. G., Dunford, N., Schwartz, J.
openaire   +2 more sources

Connectedness and Compactness of Weak Efficient Solutions for Set-Valued Vector Equilibrium Problems

Journal of Inequalities and Applications, 2008
We study the set-valued vector equilibrium problems and the set-valued vector Hartman-Stampacchia variational inequalities. We prove the existence of solutions of the two problems.
Shu-Min Yuan, Xun-Hua Gong, Bin Chen
doaj   +2 more sources

A ξ-weak Grothendieck compactness principle

Mathematical Proceedings of the Cambridge Philosophical Society, 2021
AbstractFor 0 ≤ ξ ≤ ω1, we define the notion of ξ-weakly precompact and ξ-weakly compact sets in Banach spaces and prove that a set is ξ-weakly precompact if and only if its weak closure is ξ-weakly compact. We prove a quantified version of Grothendieck’s compactness principle and the characterisation of Schur spaces obtained in [7] and [9]. For 0 ≤ ξ ≤
Beanland, Kevin, Causey, Ryan M.
openaire   +2 more sources

SPACE OF RICCI FLOWS (II)—PART A: MODULI OF SINGULAR CALABI–YAU SPACES

Forum of Mathematics, Sigma, 2017
We establish the compactness of the moduli space of noncollapsed Calabi–Yau spaces with mild singularities. Based on this compactness result, we develop a new approach to study the weak compactness of Riemannian manifolds.
XIUXIONG CHEN, BING WANG
doaj   +1 more source