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Extension of Pettis integration: Pettis operators and their integrals

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Abstract

In this note, the authors discuss the concepts of a Pettis operator, by which they mean a weak\(^*\)–weakly continuous linear operator F from a dual Banach space to an \(L_1\)-space, and of its Pettis integral, understood simply as the dual operator \(F^*\) of F. Applications to radial limits in weak Hardy spaces of vector-valued harmonic and holomorphic functions are provided.

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Acknowledgements

The first author has been supported by grant MTM2014-53009-P (MINECO, Spain). Both the authors are grateful to A. Michalak, K. Musiał, M. Nawrocki and W. Ruess for their interest in this work and numerous helpful comments. We also thank the referee for his/her interesting comments which helped us to improve the paper.

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Authors and Affiliations

  1. Departamento de Análisis Matemático, Universidad de Valencia, 46100, Burjassot, Valencia, Spain

    Oscar Blasco

  2. Faculty of Mathematics and Computer Science, A. Mickiewicz University, Umultowska 87, 61-614, Poznań, Poland

    Lech Drewnowski

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  1. Oscar Blasco
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  2. Lech Drewnowski
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Correspondence to Oscar Blasco.

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to the memory of Joe Diestel (1943–2017)

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Blasco, O., Drewnowski, L. Extension of Pettis integration: Pettis operators and their integrals. Collect. Math. 70, 267–281 (2019). https://doi.org/10.1007/s13348-018-0225-y

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  • DOI: https://doi.org/10.1007/s13348-018-0225-y

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