DE LA VALLÉE POUSSIN'S THEOREM AND WEAKLY COMPACT SETS IN ORLICZ SPACES

DOI10.1080/16073606.1994.9631762zbMath0808.46036OpenAlexW1964495497MaRDI QIDQ4304084

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Publication date: 10 October 1994

Published in: Quaestiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/16073606.1994.9631762

zbMATH Keywords

uniform integrabilityweak Banach-Saks propertyrelatively weakly compact setsDunford-Pettis theoremde la Vallée Poussin's theorem

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Compactness in topological linear spaces; angelic spaces, etc. (46A50)

Related Items (18)

ON Subspaces OF NON-Reflexive Orlicz Spaces ⋮ Non-commutative analogues of weak compactness criteria in symmetric spaces ⋮ A note on the de La Vallée Poussin criterion for uniform integrability ⋮ Weakly compact sets and weakly compact pointwise multipliers in Banach function lattices ⋮ THE WEAK DROP PROPERTY AND THE DE LA VALL´EE POUSSIN THEOREM ⋮ The structure of subspaces in Orlicz spaces lying between \(L^1\) and \(L^2\) ⋮ On quadratic integral equations in Orlicz spaces ⋮ On solutions of quadratic integral equations in Orlicz spaces ⋮ Cesaro mean convergence of martingale differences in rearrangement invariant spaces ⋮ Existence and uniqueness of weak solutions for a class of nonlinear parabolic equations ⋮ The de la Vallée Poussin theorem for vector valued measure spaces ⋮ Characterization of the Orlicz spaces whose convergence is equivalent to convergence in measure on reflexive subspaces ⋮ Countable additivity of Henstock-Dunford integrable functions and Orlicz space ⋮ On symmetric spaces with convergence in measure on reflexive subspaces ⋮ The de la Vallée-Poussin theorem and Orlicz spaces associated to a vector measure ⋮ Disjointly homogeneous Orlicz spaces revisited ⋮ \(\mathfrak{S}\)-uniform scalar integrability and strong laws of large numbers for Pettis integrable functions with values in a separable locally convex space ⋮ Rearrangement invariant spaces satisfying Dunford-Pettis criterion of weak compactness

Cites Work

• Orlicz spaces and modular spaces
• On the weak Dunford-Pettis property
• Concrete representation of abstract (M)-spaces. (A characterization of the space of continuous functions.)
• A generalization of a problem of Steinhaus
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