Extension of Pettis integration: Pettis operators and their integrals

  1. Oscar Blasco de la Cruz
  2. Lech Drewnowski
Revista:
Collectanea mathematica

ISSN: 0010-0757

Año de publicación: 2019

Volumen: 70

Fascículo: 2

Páginas: 267-281

Tipo: Artículo

DOI: 10.1007/S13348-018-0225-Y DIALNET GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Collectanea mathematica

Resumen

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 �1 -space, and of its Pettis integral, understood simply as the dual operator �∗ 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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