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A Study on Dunford–Pettis Completely Continuous Like Operators

  • M. AlikhaniEmail author
Research Paper
  • 2 Downloads

Abstract

In this article, the class of all Dunford–Pettis p-convergent operators and p-Dunford–Pettis relatively compact property on Banach spaces are investigated. Moreover, we give some conditions on Banach spaces X and Y such that the class of bounded linear operators from X to Y and some its subspaces have the p-Dunford–Pettis relatively compact property. In addition, if \( \Omega \) is a compact Hausdorff space, then we prove that dominated operators from the space of all continuous functions from K to Banach space X (in short \( C(\Omega ,X) \)) taking values in a Banach space with the p-(DPrcP) are p-convergent when X has the Dunford–Pettis property of order p. Furthermore, we show that if \( T:C(\Omega ,X)\rightarrow Y \) is a strongly bounded operator with representing measure \( m:\Sigma \rightarrow L(X,Y) \) and \( \hat{T}:B(\Omega ,X)\rightarrow Y \) is its extension, then T is Dunford–Pettis p-convergent if and only if \( \hat{T}\) is Dunford–Pettis p-convergent.

Keywords

Dunford–Pettis relatively compact property Dunford–Pettis completely continuous operators Dunford–Pettis p-convergent operators 

Mathematics Subject Classification

46B20 46B25 46B28 

Notes

Acknowledgements

This paper is part of the author’s Ph.D. thesis at the University of Isfahan. I would like to thank to Professor Jafar Zafarani and Professor Majid Fakhar, for their insight and expertise, which improved this work.

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Copyright information

© Shiraz University 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IsfahanIsfahanIran

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