The Fatou property in \(p\)-convex Banach lattices

DOI10.1016/j.jmaa.2006.04.086zbMath1121.46017OpenAlexW2074856856MaRDI QIDQ864690

Guillermo P. Curbera, Werner J. Ricker

Publication date: 12 February 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.04.086

zbMATH Keywords

vector measureBanach function spaceFatou property\(p\)-convexityspace of \(p\)-integrable functions

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) Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence (28A20) Banach lattices (46B42) Set functions, measures and integrals with values in ordered spaces (28B15)

Related Items (9)

Associate space with respect to a locally \(\sigma \)-finite measure on a \(\delta \)-ring and applications to spaces of integrable functions defined by a vector measure ⋮ The Köthe dual of an abstract Banach lattice ⋮ The dual space of \(L^p\) of a vector measure ⋮ Multiplication operators on spaces of integrable functions with respect to a vector measure ⋮ Köthe dual of Banach lattices generated by vector measures ⋮ The weak topology on \(L^p\) of a vector measure ⋮ On the Banach lattice structure of \(L^1_w\) of a vector measure on a \(\delta \)-ring ⋮ Integration for Positive Measures with Values in Quasi-Banach Lattices ⋮ On Birkhoff integrability for scalar functions and vector measures

Cites Work

• Operators into \(L^ 1\) of a vector measure and applications to Banach lattices
• Banach lattices
• Spaces of \(p\)-integrable functions with respect to a vector measure
• Banach lattices with the Fatou property and optimal domains of kernel operators
• Integration with respect to vector measures
• On integrability and summability in vector spaces
• Weak Compactness and Vector Measures
• Compactness arguments for spaces of \(p\)-integrable functions with respect to a vector measure and factorization of operators through Lebesgue-Bochner spaces
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