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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}(\\"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1606.07202","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-23T06:44:35Z","cross_cats_sorted":[],"title_canon_sha256":"990b33bf6d7e61c4e807b21de404434372edac71c53f10df23afaef516039a36","abstract_canon_sha256":"806cc1a09b9b48a9ef6fd76893b355420c8918dcb533a5411a24d625177b968d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:58.469999Z","signature_b64":"lv1DSd3CABVuxzzUrkC9kPfHWK81M8mH0HWVLgP6BrhlqTezlmO6RlRUzXJ2vrmJpB4SE4sZ4Tr8BMeI14c+Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b3de5027231bce0d0ce1fc4b7922cd3ba95c846a222c54398aaf6379b5d8013","last_reissued_at":"2026-05-18T01:11:58.469658Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:58.469658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\mathbb{K}$. 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