{"paper":{"title":"Operators on the Banach space of $p$-continuous vector-valued functions","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":"2016-06-23T06:44:35Z","abstract_excerpt":"Let $X$, $Y$, and $Z$ be Banach spaces, and let $\\alpha$ be a tensor norm. Let a bounded linear operator $S\\in\\mathcal{L}(Z,\\mathcal{L}(X,Y))$ be given. We obtain (necessary and/or sufficient) conditions for the existence of an operator $U\\in\\mathcal{L}(Z\\hat{\\otimes}_{\\alpha}X,Y)$ such that $(Sz)x = U(z\\otimes x)$, for all $z\\in Z$ and $x\\in X$, i.e., $S= U^{#}$, the associated operator to $U$. Let $\\Omega$ be a compact Hausdorff space and denote by $\\mathcal{C}(\\Omega)$ the space of continuous functions from $\\Omega$ into $\\mathbb{K}$. We apply these results to $S\\in\\mathcal{L}(\\mathcal{C}(\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07202","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"}