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Strongly \((p,\sigma ) \)-Lipschitz operators

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Abstract

This work aims to define a new class of operators, called strongly \(\left( p,\sigma \right) \)-Lipschitz map**s. We prove a Pietsch type domination/factorization theorem for this class of operators and show it characterizes Lipschitz map**s whose Lipschitz conjugates are absolutely \( (p^{*};\sigma )\)-summing.

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Acknowledgements

We would like to express our gratitude to the two referees for their carefully reading of the manuscript, valuable comments constructive suggestions, which have improved the final version of the paper. A. Belacel and A. Bougoutaia acknowledges with thanks the support of the Ministère de l’Enseignament Supérieur et de la Recherche Scientifique (Algeria), and Renato Macedo is partially supported by Capes.

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Authors and Affiliations

  1. Laboratory of Pure and Applied Mathematics (LPAM), University of Laghouat, Laghouat, Algeria

    Amar Bougoutaia & Amar Belacel

  2. Departamento de Matemática, Universidade Federal da Paraíba, 58.051-900, João Pessoa, Brazil

    Renato Macedo

Authors
  1. Amar Bougoutaia
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  2. Amar Belacel
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  3. Renato Macedo
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Corresponding author

Correspondence to Amar Bougoutaia.

Additional information

Communicated by Yuri Karlovich.

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Bougoutaia, A., Belacel, A. & Macedo, R. Strongly \((p,\sigma ) \)-Lipschitz operators. Adv. Oper. Theory 8, 20 (2023). https://doi.org/10.1007/s43036-023-00248-y

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