{"paper":{"title":"Commutators and linear spans of projections in certain finite C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Ping W. Ng, Shuang Zhang, Victor Kaftal","submitted_at":"2012-08-09T15:27:30Z","abstract_excerpt":"Assume that A is a unital separable simple C*-algebra with real rank zero, stable rank one, strict comparison of projections, and that its tracial simplex T(A) has a finite number of extremal points.\n  We prove that every self-adjoint element a in A in the kernel of all tracial states is the sum of two commutators in A and that every positive element of A is a linear combination of projections with positive coefficients.\n  Assume that A is as above but \\sigma-unital. Then an element (resp. a positive element) a of A is a linear combination (resp. a linear combination with positive coefficients"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1949","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"}