Spaces of Vector‐Valued Integrable Functions and Localization of Bounded Subsets

DOI10.1002/MANA.19951740109zbMath0828.46035OpenAlexW1991584634MaRDI QIDQ4845831

Fernando Mayoral, Pedro J. Paúl, Miguel Florencio

Publication date: 17 September 1995

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.19951740109

zbMATH Keywords

Radon-Nikodym propertyvector-valued sequencesspaces of vector-valued functionsabsolutely integrable Lusin-measurable functions with values in a locally convex spaceintegral representation of continuous linear operatorsproperty (B) of Pietsch

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) Spaces of vector- and operator-valued functions (46E40)

Related Items (4)

Testing on null sequences is enough for Bochner integrability ⋮ \((DF)\)-spaces of vector-valued integrable functions ⋮ DIEUDONNÉ—KÖTHE DUALITY FOR VECTOR—VALUED FUNCTION SPACES: LOCALIZATION OF BOUNDED SETS AND BARRELLEDNESS ⋮ Aspects of control theory on infinite-dimensional Lie groups and \(G\)-manifolds

Cites Work

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• An abstract Banach-Steinhaus theorem and applications to function spaces
• On the completeness of \(L^\alpha(E)\) for locally convex spaces
• Barrelledness and bornological conditions on spaces of vector-valued \(\mu\)-simple functions
• Dual density conditions in (DF)-spaces. I
• Inductive limits of spaces of vector-valued integrable functions

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