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Factorization of Operators Through Orlicz Spaces

  • M. Mastyło
  • E. A. Sánchez Pérez
Article

Abstract

We study factorization of operators between quasi-Banach spaces. We prove the equivalence between certain vector norm inequalities and the factorization of operators through Orlicz spaces. As a consequence, we obtain the Maurey–Rosenthal factorization of operators into \(L_p\)-spaces. We give several applications. In particular, we prove a variant of Maurey’s Extension Theorem.

Keywords

Factorization Banach function lattice Banach envelope Orlicz space 

Mathematics Subject Classification

46E30 47B38 46B42 

Notes

Acknowledgments

The research of the first author was supported by the National Science Centre (NCN), Poland, Grant No. 2011/01/B/ST1/06243. The research of the second author was supported by Ministerio de Economía y Competitividad, Spain, under project #MTM2012-36740-C02-02.

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Copyright information

© Malaysian Mathematical Sciences Society and Universiti Sains Malaysia 2015

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceA. Mickiewicz UniversityPoznanPoland
  2. 2.Institute of Mathematics Polish Academy of SciencesPoznanPoland
  3. 3.Instituto Universitario de Matemática Pura y AplicadaUniversitat Politècnica de ValènciaValenciaSpain

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