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Factorization of Operators Through Orlicz Spaces

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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.

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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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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, A. Mickiewicz University, Poznan, Poland

    M. Mastyło

  2. Institute of Mathematics Polish Academy of Sciences, Poznan, Poland

    M. Mastyło

  3. Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Valencia, Spain

    E. A. Sánchez Pérez

Authors
  1. M. Mastyło
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  2. E. A. Sánchez Pérez
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Correspondence to E. A. Sánchez Pérez.

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Communicated by Mohammad Sal Moslehian, Ph.D.

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Mastyło, M., Sánchez Pérez, E.A. Factorization of Operators Through Orlicz Spaces. Bull. Malays. Math. Sci. Soc. 40, 1653–1675 (2017). https://doi.org/10.1007/s40840-015-0158-5

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  • DOI: https://doi.org/10.1007/s40840-015-0158-5

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