{"paper":{"title":"Traceability of positive integral operators in the absence of a metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ana P. Peron, Mario H. Castro, Valdir A. Menegatto","submitted_at":"2012-01-10T17:19:04Z","abstract_excerpt":"We investigate the traceability of positive integral operators on $L^2(X,\\mu)$ when $X$ is a Hausdorff locally compact second countable space and $\\mu$ is a non-degenerate, $\\sigma$-finite and locally finite Borel measure. This setting includes other cases proved in the literature, for instance the one in which $X$ is a compact metric space and $\\mu$ is a special finite measure. The results apply to spheres, tori and other relevant subsets of the usual space $\\mathbb{R}^m$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2117","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"}