The weak topology on \(L^p\) of a vector measure

DOI10.1016/j.topol.2007.12.014zbMath1151.28014OpenAlexW1994391667MaRDI QIDQ930751

I. Ferrando, José Rodríguez

Publication date: 1 July 2008

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2007.12.014

zbMATH Keywords

weak convergencevector measureWCG spacespace of integrable functionsJames boundary

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) Vector-valued set functions, measures and integrals (28B05) Vector-valued measures and integration (46G10)

Related Items (11)

Topological dual systems for spaces of vector measure \(p\)-integrable functions ⋮ 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 ⋮ Product spaces generated by bilinear maps and duality ⋮ Differentiability of \(L^p\) of a vector measure and applications to the Bishop-Phelps-Bollobás property ⋮ On the smoothness of \(L^p\) of a positive vector measure ⋮ The dual space of \(L^p\) of a vector measure ⋮ Summability in L1 of a vector measure ⋮ Köthe dual of Banach lattices generated by vector measures ⋮ Factorization theorems for homogeneous maps on Banach function spaces and approximation of compact operators ⋮ TENSOR PRODUCT REPRESENTATION OF THE (PRE)DUAL OF THE L^p-SPACE OF A VECTOR MEASURE ⋮ Factorization theorem for 1-summing operators

Cites Work

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• Operators into \(L^ 1\) of a vector measure and applications to Banach lattices
• The Fatou property in \(p\)-convex Banach lattices
• Spaces of integrable functions with respect to a vector measure and factorizations through \(L^{p}\) and Hilbert spaces
• Boundaries of a convex set and interpolation sets
• Banach lattices
• Some remarks on weakly compactly generated Banach spaces
• Geometry of Banach spaces. Selected topics
• The dual space of \({\mathcal L}^ 1(\mu)\) for a vector measure \(\mu\)
• When \(L^ 1\) of a vector measure is an AL-space
• Vector measure Maurey--Rosenthal-type factorizations and \(\ell\)-sums of \(L^1\)-spaces
• Spaces of \(p\)-integrable functions with respect to a vector measure
• Integration with respect to vector measures
• James boundaries and σ-fragmented selectors
• Vector measure duality and tensor product representations of $L_p$-spaces of vector measures
• Banach Space Properties of L 1 of a Vector Measure
• Functional analysis and infinite-dimensional geometry
• 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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