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FACTORIZATION OF OPERATORS THROUGH SUBSPACES OF $L^{1}$-SPACES

Part of: Linear function spaces and their duals Special classes of linear operators Measures, integration, derivative, holomorphy

Published online by Cambridge University Press:  08 November 2016

J. M. CALABUIG ,
J. RODRÍGUEZ  and
E. A. SÁNCHEZ-PÉREZ
J. M. CALABUIG
Affiliation:
Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain email jmcalabu@mat.upv.es
J. RODRÍGUEZ*
Affiliation:
Departamento de Matemática Aplicada, Facultad de Informática, Universidad de Murcia, 30100 Espinardo (Murcia), Spain email joserr@um.es
E. A. SÁNCHEZ-PÉREZ
Affiliation:
Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain email easancpe@mat.upv.es
*
✉joserr@um.es
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Abstract

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We analyze domination properties and factorization of operators in Banach spaces through subspaces of $L^{1}$-spaces. Using vector measure integration and extending classical arguments based on scalar integral bounds, we provide characterizations of operators factoring through subspaces of $L^{1}$-spaces of finite measures. Some special cases involving positivity and compactness of the operators are considered.

Keywords

Banach function spacepositive operatorcompact operatorfactorizationL1 -spacevector measure

MSC classification

Primary: 46E30: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Secondary: 46G10: Vector-valued measures and integration 47B07: Operators defined by compactness properties 47B65: Positive operators and order-bounded operators
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 103 , Issue 3 , December 2017 , pp. 313 - 328
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

Footnotes

Research supported by MINECO/FEDER under projects MTM2014-53009-P (J. M. Calabuig), MTM2014-54182-P (J. Rodríguez) and MTM2012-36740-C02-02 (E. A. Sánchez-Pérez).

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