{"paper":{"title":"Locally convex quasi $C^*$-normed algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.OA"],"primary_cat":"math-ph","authors_text":"Atsushi Inoue, Camillo TRapani, Fabio Bagarello, Maria Fragoulopoulou","submitted_at":"2012-07-09T11:59:27Z","abstract_excerpt":"If $\\ca_0[|\\cdot|_0]$ is a $\\cs$-normed algebra and $\\tau$ a locally convex topology on $\\ca_0$ making its multiplication separately continuous, then $\\widetilde{\\ca_0}[\\tau]$ (completion of $\\ca_0[\\tau]$) is a locally convex quasi *-algebra over $\\ca_0$, but it is not necessarily a locally convex quasi *-algebra over the $\\cs$-algebra $\\widetilde{\\ca_0}[|\\cdot|_0]$ (completion of $\\ca_0[|\\cdot|_0]$). In this article, stimulated by physical examples, we introduce the notion of a locally convex quasi $\\cs$-normed algebra, aiming at the investigation of $\\widetilde{\\ca_0}[\\tau]$; in particular, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2015","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"}