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

2019/05/09 by Alikhani, M.
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1905.03576

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 adjoint every \(p\)-convergent operator \(T: X → Y\) 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. The stability of reciprocal Dunford-Pettis property of order \(p\) for the projective tensor product is given.

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