Spaces of \(p\)-integrable functions with respect to a vector measure

DOI10.1007/s11117-005-0016-zzbMath1111.46018OpenAlexW1982149690MaRDI QIDQ2499021

Carmen Sáez, Antonio Fernández, Fernando Mayoral, Francisco Naranjo, Enrique Alfonso Sánchez-Pérez

Publication date: 14 August 2006

Published in: Positivity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11117-005-0016-z

zbMATH Keywords

vector measureintegration\(L^p\)-spacesfunction spaces\(L\)-weakly compact operators

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 measures and integration (46G10)

Related Items

Optimal extensions of compactness properties for operators on Banach function spaces ⋮ 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 ⋮ Strong factorization of operators on spaces of vector measure integrable functions and unconditional convergence of series ⋮ Product spaces generated by bilinear maps and duality ⋮ Algebra structure for \(L^p\) of a vector measure ⋮ The Fatou property in \(p\)-convex Banach lattices ⋮ Integration of vector-valued functions with respect to vector measures defined on \(\delta \)-rings ⋮ A nonlinear approach to signal processing by means of vector measure orthogonal functions ⋮ Strongly embedded subspaces of \(p\)-convex Banach function spaces ⋮ Spaces of integrable functions with respect to a vector measure and factorizations through \(L^{p}\) and Hilbert spaces ⋮ On the smoothness of \(L^p\) of a positive vector measure ⋮ The dual space of \(L^p\) of a vector measure ⋮ Real interpolation method on spaces of scalar integrable functions with respect to vector measures ⋮ Multiplication operators on spaces of integrable functions with respect to a vector measure ⋮ Complex interpolation of 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 ⋮ Complex interpolation of operators and optimal domains ⋮ On the Banach lattice structure of \(L^1_w\) of a vector measure on a \(\delta \)-ring ⋮ On the norm with respect to vector measures of the solution of an infinite system of ordinary differential equations ⋮ Weighted Hardy inequalities, real interpolation methods and vector measures ⋮ Lorentz spaces of vector measures and real interpolation of operators ⋮ A bilinear version of Orlicz-Pettis theorem ⋮ On the optimal domain of the Laplace transform ⋮ Interpolation between weighted Lorentz spaces with respect to a vector measure ⋮ Complex interpolation of Orlicz spaces with respect to a vector measure ⋮ A note on real interpolation of \(L^p\)-spaces of vector measures on \(\delta\)-rings ⋮ Lattice copies of \(\ell^2\) in \(L^1\) of a vector measure and strongly orthogonal sequences ⋮ Complex interpolation of \(L^p\)-spaces of vector measures on \(\delta\)-rings ⋮ Interpolation of vector measures ⋮ Generalized perfect spaces ⋮ Factorization theorems for homogeneous maps on Banach function spaces and approximation of compact operators ⋮ Vector measure Maurey--Rosenthal-type factorizations and \(\ell\)-sums of \(L^1\)-spaces ⋮ Reflexivity of function spaces associated to a \(\sigma\)-finite vector measure ⋮ The de la Vallée-Poussin theorem and Orlicz spaces associated to a vector measure ⋮ Norming sets and integration with respect to vector measures ⋮ Ordered representations of spaces of integrable functions ⋮ The space of scalarly integrable functions for a Fréchet-space-valued measure ⋮ TENSOR PRODUCT REPRESENTATION OF THE (PRE)DUAL OF THE L^p-SPACE OF A VECTOR MEASURE ⋮ On Birkhoff integrability for scalar functions and vector measures ⋮ Multiplication operators on vector measure Orlicz spaces ⋮ The Gould integral in Banach lattices

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Operators into \(L^ 1\) of a vector measure and applications to Banach lattices
• Banach lattices
• Weakly sequentially complete Fréchet spaces of integrable functions
• The dual space of \({\mathcal L}^ 1(\mu)\) for a vector measure \(\mu\)
• When \(L^ 1\) of a vector measure is an AL-space
• Rybakov's theorem for vector measures in Fréchet spaces
• Vector measure orthonormal functions and best approximation for the 4-norm
• Spaces of integrable functions with respect to vector measures of convex range and factorization of operators from \(L_p\)-spaces.
• On quasi-complemented subspaces of Banach spaces, with an appendix on compactness of operators from \(L^{p}(\mu)\) to \(L^{r}(\nu)\)
• Integration with respect to vector measures
• Spaces \(L_2(\lambda)\) of a positive vector measure \(\lambda\) and generalized Fourier coefficients
• Compactness of the integration operator associated with a vector measure
• Weak Compactness and Vector Measures
• Separability of the L¹-space of a vector measure
• Compactness properties of the integration mapassociated with a vector measure
• Banach Space Properties of L 1 of a Vector Measure
• Compactness arguments for spaces of \(p\)-integrable functions with respect to a vector measure and factorization of operators through Lebesgue-Bochner spaces