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A study of reciprocal Dunford–Pettis-like properties on Banach spaces

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Abstract

In this article, we study the relationship between p- (V) subsets and p-\( (V^{*})\) subsets of dual spaces. We investigate the Banach space X with the property that the adjoint of every p-convergent operator \( T:X\rightarrow Y \) is weakly q-compact, for every Banach space Y. Moreover, we define the notion of q-reciprocal Dunford–Pettis\( ^{*} \) property of order p on Banach spaces and obtain a characterization of Banach spaces with this property. Also, the stability of reciprocal Dunford–Pettis property of order p for projective tensor product is given.

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Acknowledgements

I would like to thank the anonymous reviewer for careful and thorough reading of this manuscript and for the thoughtful comments and constructive suggestions, which help to improve the quality of this manuscript. This paper is a part of the author’s PhD. thesis at the University of Isfahan. Special thanks goes to my supervisors; Prof. Jafar Zafarani and Prof. Majid Fakhar, for their usefull comments and suggestions which improved this work, significantly.

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  1. Department of Mathematics, University of Isfahan, 81745-163, Isfahan, Iran

    Morteza Alikhani

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  1. Morteza Alikhani
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Correspondence to Morteza Alikhani.

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Communicated by Miguel Martin.

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Alikhani, M. A study of reciprocal Dunford–Pettis-like properties on Banach spaces. Adv. Oper. Theory 5, 27–38 (2020). https://doi.org/10.1007/s43036-019-00003-2

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