Factorizing operators on Banach function spaces through spaces of multiplication operators

DOI10.1016/j.jmaa.2009.10.034zbMath1191.47023OpenAlexW2020755220MaRDI QIDQ847055

Enrique Alfonso Sánchez-Pérez, Jose M. Calabuig, Olvido Delgado

Publication date: 12 February 2010

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.2009.10.034

zbMATH Keywords

vector measuresmultiplication operatorsBanach function spacesfactorisation of operators

Mathematics Subject Classification ID

Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators (47A68) Linear operators on function spaces (general) (47B38) Vector-valued measures and integration (46G10)

Related Items (15)

OPTIMAL EXTENSIONS FOR POSITIVE ORDER CONTINUOUS OPERATORS ON BANACH FUNCTION SPACES ⋮ Strong extensions for \(q\)-summing operators acting in \(p\)-convex Banach function spaces for \(1 \leq p \leq q\) ⋮ Optimal extensions for \(p\)th power factorable operators ⋮ Factorization theorems for multiplication operators on Banach function spaces ⋮ Maharam-type kernel representation for operators with a trigonometric domination ⋮ Optimal extensions of Lipschitz maps on metric spaces of measurable functions ⋮ Factorizing kernel operators ⋮ Optimal extension of positive order continuous operators with values in quasi-Banach lattices ⋮ On the Banach lattice structure of \(L^1_w\) of a vector measure on a \(\delta \)-ring ⋮ Extension of Lipschitz-type operators on Banach function spaces ⋮ Extrapolation theorems for \((p,q)\)-factorable operators ⋮ A Komlós theorem for abstract Banach lattices of measurable functions ⋮ Factorization theorems for homogeneous maps on Banach function spaces and approximation of compact operators ⋮ Extending and factorizing bounded bilinear maps defined on order continuous Banach function spaces ⋮ Tensor product representation of Köthe-Bochner spaces and their dual spaces

Cites Work

• Set-functions and factorization
• Optimal domain for the Hardy operator
• Optimal domain and integral extension of operators, acting in function spaces
• Factorization of operators through \(L_{p\infty}\) or \(L_{p1}\) and non- commutative generalizations
• \(L^1\)-spaces of vector measures defined on \(\delta\)-rings
• The integration theory of Banach space valued measures and the Tonelli- Fubini theorems. I: Scalar-valued measures on \(\delta\)-rings
• Strong additivity, absolute continuity, and compactness in spaces of measures
• The integration theory of Banach space valued measures and the Tonelli- Fubini theorems. II: Pettis integration
• Banach lattices with the Fatou property and optimal domains of kernel operators
• On integrability and summability in vector spaces
• Strong factorization of operators on spaces of vector measure integrable functions and unconditional convergence of series
• Optimal domains for kernel operators on [0,∞)×[0,∞)
• Variants of the Maurey-Rosenthal theorem for quasi Köthe function spaces
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