{"paper":{"title":"Vector duality via conditional extension of dual pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Asgar Jamneshan, Michael Kupper, Samuel Drapeau","submitted_at":"2016-08-31T02:27:14Z","abstract_excerpt":"A Fenchel-Moreau type duality for proper convex and lower semi-continuous functions $f\\colon X\\to \\overline{L^0}$ is established where $(X,Y,\\langle \\cdot,\\cdot \\rangle)$ is a dual pair of Banach spaces and $\\overline{L^0}$ is the set of all extended real-valued measurable functions. We provide a concept of lower semi-continuity which is shown to be equivalent to the existence of a dual representation in terms of elements in the Bochner space $L^0(Y)$. To derive the duality result, several conditional completions and extensions are constructed.\n  This is an earlier version of arXiv e-print 170"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08709","kind":"arxiv","version":4},"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"}