On p-Dunford integrable functions with values in Banach spaces

Let (Ω,Σ,μ) be a complete probability space, X a Banach space and 1≤p<∞. In this paper we discuss several aspects of p-Dunford integrable functions f:Ω→X. Special attention is paid to the compactness of the Dunford operator of f. We also study the p-Bochner integrability of the composition u∘f:Ω→Y, where u is a p-summing operator from X to another Banach space Y. Finally, we also provide some tests of p-Dunford integrability by using w⁎-thick subsets of X⁎.