{"paper":{"title":"The Bartle-Dunford-Schwartz and the Dinculeanu-Singer theorems revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"C\\'andido Pi\\~neiro, Eve Oja, Fernando Mu\\~noz","submitted_at":"2016-12-21T20:46:41Z","abstract_excerpt":"Let $X$ and $Y$ be Banach spaces and let $\\Omega$ be a compact Hausdorff space. Denote by $\\mathcal{C}_{p}(\\Omega,X)$ the space of $p$-continous $X$-valued functions, $1\\leq p\\leq \\infty$. For operators $S\\in\\mathcal{L}(\\mathcal{C}(\\Omega),\\mathcal{L}(X,Y))$ and $U\\in\\mathcal{L}(\\mathcal{C}_{p}(\\Omega,X),Y)$, we establish integral representation theorems with respect to a vector measure $m:\\Sigma\\rightarrow \\mathcal{L}(X,Y^{**})$, where $\\Sigma$ denotes the $\\sigma$-algebra of Borel subsets of $\\Omega$. The first theorem extends the classical Bartle-Dunford-Schwartz representation theorem. It "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07312","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"}