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(p, q)-Regular operators between Banach lattices

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Abstract

We study the class of (p, q)-regular operators between quasi-Banach lattices. In particular, a representation of this class as the dual of a certain tensor norm for Banach lattices is given. We also provide some factorization results for (p, q)-regular operators yielding new Marcinkiewicz–Zygmund type inequalities for Banach function spaces. An extension theorem for \((q, \infty )\)-regular operators defined on a subspace of \(L_q\) is also given.

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Authors and Affiliations

  1. Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022, Valencia, Spain

    Enrique A. Sánchez Pérez

  2. Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM) Consejo Superior de Investigaciones Científicas, C/ Nicolás Cabrera, 13–15, Campus de Cantoblanco UAM, 28049, Madrid, Spain

    Pedro Tradacete

Authors
  1. Enrique A. Sánchez Pérez
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  2. Pedro Tradacete
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Correspondence to Pedro Tradacete.

Additional information

Communicated by K. Gröchenig.

E. A. Sánchez Pérez gratefully acknowledges support of Spanish Ministerio de Economía, Industria y Competitividad and FEDER under Project MTM2016-77054-C2-1-P. P. Tradacete gratefully acknowledges support of Spanish Ministerio de Economía, Industria y Competitividad through Grants MTM2016-76808-P and MTM2016-75196-P, the “Severo Ochoa Programme for Centres of Excellence in R&D” (SEV-2015-0554), and Grupo UCM 910346. The authors wish to thank the anonymous referee for his/her careful reading of the manuscript.

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Sánchez Pérez, E.A., Tradacete, P. (p, q)-Regular operators between Banach lattices. Monatsh Math 188, 321–350 (2019). https://doi.org/10.1007/s00605-018-1247-y

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