OPTIMAL EXTENSIONS FOR POSITIVE ORDER CONTINUOUS OPERATORS ON BANACH FUNCTION SPACES

DOI10.1017/S0017089513000384zbMath1308.46054MaRDI QIDQ2921053

Olvido Delgado

Publication date: 30 September 2014

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

vector measureintegrationpositive operator\(\delta\)-ringkernel operatoroptimal extension

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) Banach lattices (46B42) Vector-valued measures and integration (46G10) Positive linear operators and order-bounded operators (47B65)

Related Items (4)

Optimal extensions of Lipschitz maps on metric spaces of measurable functions ⋮ Optimal extension of positive order continuous operators with values in quasi-Banach lattices ⋮ Kantorovich-Wright integration and representation of vector lattices ⋮ Integration for Positive Measures with Values in Quasi-Banach Lattices

Cites Work

• Unnamed Item
• Factorizing operators on Banach function spaces through spaces of multiplication operators
• Optimal domain for the Hardy operator
• \(L^1\)-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
• Optimal domains and integral representations of convolution operators in \(L^p(G)\)
• The integration theory of Banach space valued measures and the Tonelli- Fubini theorems. II: Pettis integration
• Optimal domains for the kernel operator associated with Sobolev's inequality
• Volterra Convolution Operators with Values in Rearrangement Invariant Spaces

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