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arXiv · 1611.08087

On $p$-Dunford integrable functions with values in Banach spaces

J. M. Calabuig·J. Rodríguez·P. Rueda·E. A. Sánchez-Pérez
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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 $f:\Omega \to X$. Special attention is paid to the compactness of the Dunford operator of $f$. We also study the $p$-Bochner integrability of the composition $u\circ f:\Omega \to Y$, 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 $X^*$.

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J. M. Calabuig, J. Rodríguez, P. Rueda, E. A. Sánchez-Pérez. 2016-11-24. On $p$-Dunford integrable functions with values in Banach spaces. https://arxiv.org/abs/1611.08087

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