Weak compactness in 𝐿¹(𝜇,𝑋)

Díaz, Santiago

doi:10.1090/s0002-9939-96-03336-9

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Bochner Integrals Of Multifunctions1

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Cited by 9 publications

(1 citation statement)

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“…Well-dominance provides a Bochner integral analogue of the Dunford-Pettis criterion for the relative weak compactness in L 1 (µ, E). For the development of the weak compactness in L 1 (µ, E), see also [23,26,44,82,84].…”

Section: Bochner Integrals Of Multifunctionsmentioning

confidence: 99%

Fatou's Lemma, Galerkin Approximations and the Existence of Walrasian Equilibria in Infinite Dimensions

Khan,

Sagara

2016

Preprint

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This essay has three objectives: (i) to report recent generalizations of Fatou's lemma to multi-functions taking values in a Banach space, and framed in terms of both Bochner and Gelfand integration; (ii) to delineate the importance of Galerkin approximations in Walrasian general equilibrium theory with a continuum of agents and commodities; and thereby (iii) to present two new results on the existence of a Walrasian equilibrium in economies where the continuum of agents is formalized as a saturated measure space.

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Section: Bochner Integrals Of Multifunctionsmentioning

confidence: 99%

Fatou's Lemma, Galerkin Approximations and the Existence of Walrasian Equilibria in Infinite Dimensions

Khan,

Sagara

2016

Preprint

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Weighted Composition Operators on Hardy Spaces

Contreras

Hernández-Díaz

2001

Journal of Mathematical Analysis and Applications

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Ž .Let , be analytic functions defined on ‫,ބ‬ such that ‫ބ‬ : ‫.ބ‬ The operator Ž . given by f ¬ f ( is called a weighted composition operator. In this paper we deal with the boundedness, compactness, weak compactness, and complete continu-Ž . ity of weighted composition operators on Hardy spaces H 1 F p -ϱ . In p particular, we prove that such an operator is compact on H if and only if it is 1 weakly compact on this space. This result depends on a technique which passes the weak compactness from an operator T to operators dominated in norm by T.

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Stability Properties II

Lin

2004

Köthe-Bochner Function Spaces

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Weak compactness in 𝐿¹(𝜇,𝑋)

Abstract: Abstract. We characterize weak compactness and weak conditional compactness of subsets of L 1 (µ, X) in terms of regular methods of summability. We also study when these results still hold using only convergence in the sense of Cesàro.

Cited by 9 publications

References 15 publications

Fatou's Lemma, Galerkin Approximations and the Existence of Walrasian Equilibria in Infinite Dimensions

Fatou's Lemma, Galerkin Approximations and the Existence of Walrasian Equilibria in Infinite Dimensions

Weighted Composition Operators on Hardy Spaces

Stability Properties II

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