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Aron–Berner extensions of almost Dunford–Pettis multilinear operators

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Abstract

We study when Aron–Berner extensions of (separately) almost Dunford–Pettis multilinear operators between Banach lattices are (separately) almost Dunford–Pettis. For instance, for a \(\sigma \)-Dedekind complete Banach lattice F containing a copy of \(\ell _\infty \), we characterize the Banach lattices \(E_1, \ldots , E_m\) for which every continuous m-linear operator from \(E_1 \times \cdots \times E_m\) to F admits an almost Dunford–Pettis Aron–Berner extension. Illustrative examples are provided.

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Acknowledgements

The authors thank the reviewer for the careful reading and the invaluable suggestions that improved the final presentation of the paper.

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Authors and Affiliations

  1. Faculdade de Matemática, Universidade Federal de Uberlândia, Uberlândia, 38.400-902, Brazil

    Geraldo Botelho

  2. Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, 05.508-090, Brazil

    Luis Alberto Garcia

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  1. Geraldo Botelho
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  2. Luis Alberto Garcia
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Correspondence to Geraldo Botelho.

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Communicated by Michael Kunzinger.

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Geraldo Botelho supported by Fapemig Grants PPM-00450-17, RED-00133-21 and APQ-01853-23. Luis Alberto Garcia supported by a CAPES scholarship

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Botelho, G., Garcia, L.A. Aron–Berner extensions of almost Dunford–Pettis multilinear operators. Monatsh Math 203, 563–581 (2024). https://doi.org/10.1007/s00605-023-01936-w

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