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Positivity

, Volume 23, Issue 1, pp 75–88 | Cite as

Factorization through Lorentz spaces for operators acting in Banach function spaces

  • E. A. Sánchez PérezEmail author
Article
  • 28 Downloads

Abstract

We show a factorization through Lorentz spaces for Banach-space-valued operators defined in Banach function spaces. Although our results are inspired in the classical factorization theorem for operators from \(L^s\)-spaces through Lorentz spaces \(L^{q,1}\) due to Pisier, our arguments are different and essentially connected with Maurey’s theorem for operators that factor through \(L^p\)-spaces. As a consequence, we obtain a new characterization of Lorentz \(L^{q,1}\)-spaces in terms of lattice geometric properties, in the line of the (isomorphic) description of \(L^p\)-spaces as the unique ones that are p-convex and p-concave.

Keywords

Lorentz space Factorization Operator Banach lattice Concavity 

Mathematics Subject Classification

46E30 47B38 46B42 

Notes

Acknowledgements

Funding was provided by Secretaría de Estado de Investigación, Desarrollo e Innovación and FEDER (Grant No. MTM2016-77054-c2-1-P).

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Instituto Universitario de Matemática Pura y AplicadaUniversitat Politècnica de ValènciaValenciaSpain

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