{"paper":{"title":"Positive representations of $C_0(X)$. I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Frejanne Ruoff, Marcel de Jeu","submitted_at":"2015-04-26T13:35:24Z","abstract_excerpt":"We introduce the notion of a positive spectral measure on a $\\sigma$-algebra, taking values in the positive projections on a Banach lattice. Such a measure generates a bounded positive representation of the bounded measurable functions. If $X$ is a locally compact Hausdorff space, and $\\pi$ is a positive representation of $C_0(X)$ on a KB-space, then $\\pi$ is the restriction to $C_0(X)$ of such a representation generated by a unique regular positive spectral measure on the Borel $\\sigma$-algebra of $X$. The relation between a positive representation of $C_0(X)$ on a Banach lattice and -- if it"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06820","kind":"arxiv","version":2},"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"}