Rearrangement invariant spaces satisfying Dunford-Pettis criterion of weak compactness

DOI10.1090/CONM/733/14732zbMath1443.46018OpenAlexW2965496515MaRDI QIDQ5241855

Serguei V. Astashkin

Publication date: 4 November 2019

Published in: Functional Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/conm/733/14732

zbMATH Keywords

rearrangement invariant spaceLorentz spaceOrlicz spaceMarcinkiewicz spaceweakly compact setpositive Schur propertystrongly embedded subspacemartingale differencereflexive subspaceequi-integrable setequi-absolutely continuous norms

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) Banach lattices (46B42) Compactness in Banach (or normed) spaces (46B50)

Related Items (5)

Non-commutative analogues of weak compactness criteria in symmetric spaces ⋮ Weakly compact sets and weakly compact pointwise multipliers in Banach function lattices ⋮ On disjointly homogeneous Orlicz-Lorentz spaces ⋮ Disjointly homogeneous Orlicz spaces revisited ⋮ ℓ₂-strictly singular operators on the predual of a hyperfinite von Neumann algebra

Cites Work

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• Cesaro mean convergence of martingale differences in rearrangement invariant spaces
• On the weak Dunford-Pettis property
• Banach lattices
• On symmetric spaces with convergence in measure on reflexive subspaces
• Disjointly homogeneous Banach lattices: duality and complementation
• Bases, lacunary sequences and complemented subspaces in the spaces $L_{p}$
• A note on the positive Schur property
• Reflexive subspaces of some Orlicz spaces
• Cesaro Convergence of Martingale Difference Sequences and the Banach-Saks and Szlenk Theorems
• A Characterization of Banach Spaces Containing l ¹
• DE LA VALLÉE POUSSIN'S THEOREM AND WEAKLY COMPACT SETS IN ORLICZ SPACES
• On the convergence in mean of martingale difference sequenceS
• Relations Between Function Spaces
• Linear Operations on Summable Functions

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