{"paper":{"title":"On $p$-Dunford integrable functions with values in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"E.A. S\\'anchez-P\\'erez, J.M. Calabuig, J. Rodr\\'iguez, P. Rueda","submitted_at":"2016-11-24T07:44:19Z","abstract_excerpt":"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 $X^*$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08087","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}