This is an announcement for the paper “On p-Dunford integrable functions with values in Banach spaces” by J.M. Calabuighttps://arxiv.org/find/math/1/au:+Calabuig_J/0/1/0/all/0/1, J. Rodríguezhttps://arxiv.org/find/math/1/au:+Rodriguez_J/0/1/0/all/0/1, P. Ruedahttps://arxiv.org/find/math/1/au:+Rueda_P/0/1/0/all/0/1, E.A. Sánchez-Pérezhttps://arxiv.org/find/math/1/au:+Sanchez_Perez_E/0/1/0/all/0/1.
Abstract: Let $(\Omega, \Sigma, \mu)$ be a complete probability space, $X$ a Banach space and $1\leq p<\infty$. In this paper we discuss several aspects of $p$-Dunford integrable functions $f: \Omega\rightarrow X$. Special attention is paid to the compactness of the Dunford operator of $f$. We also study the $p$-Bochner integrability of the composition $u\circ f: \Omega\rightarrow Y$, 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 $X^*$.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1611.08087