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Collectanea Mathematica

, Volume 70, Issue 2, pp 267–281 | Cite as

Extension of Pettis integration: Pettis operators and their integrals

  • Oscar BlascoEmail author
  • Lech Drewnowski
Article
  • 51 Downloads

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.

Keywords

Pettis integral Pettis operator Weak\(^*\)–weakly continuous operator Weak Hardy space 

Mathematics Subject Classification

46G10 28B05 

Notes

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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Copyright information

© Universitat de Barcelona 2018

Authors and Affiliations

  1. 1.Departamento de Análisis MatemáticoUniversidad de ValenciaBurjassot, ValenciaSpain
  2. 2.Faculty of Mathematics and Computer ScienceA. Mickiewicz UniversityPoznańPoland

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