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Cohen positive strongly p-summing and p-convex multilinear operators

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Abstract

The aim of this work is to give and study the notion of Cohen positive p-summing multilinear operators. We prove a natural analog of the Pietsch domination theorem for these classes and characterize their conjugates. As an application, we generalize a result due to Bu and Shi (J. Math. Anal. Appl. 401:174–181, 2013), and we compare this class with the class of multiple p-convex m-linear operators.

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Acknowledgements

The authors are very grateful to an anonymous referee for pointing out some mistakes in the previous version of this paper, and for a careful reading that led to many improvements.

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Authors and Affiliations

  1. Faculty of Exact Sciences and the Sciences of Nature and Life, University of Mohamed Khider, B.P.145, Biskra, 07000, Algeria

    Amar Bougoutaia

  2. Laboratory of Pure and Applied Mathematics (LMPA), University of Laghouat, Laghouat, Algeria

    Amar Belacel

Authors
  1. Amar Bougoutaia
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  2. Amar Belacel
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Correspondence to Amar Belacel.

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Bougoutaia, A., Belacel, A. Cohen positive strongly p-summing and p-convex multilinear operators. Positivity 23, 379–395 (2019). https://doi.org/10.1007/s11117-018-0612-3

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  • DOI: https://doi.org/10.1007/s11117-018-0612-3

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