{"paper":{"title":"Exponential rank and exponential length for Z-stable simple C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Huaxin Lin","submitted_at":"2013-01-03T00:02:22Z","abstract_excerpt":"Let $A$ be a unital separable simple ${\\cal Z}$-stable C*-algebra which has rational tracial rank at most one and let $u\\in U_0(A),$ the connected component of the unitary group of $A.$ We show that, for any $\\epsilon>0,$ there exists a self-adjoint element $h\\in A$ such that $$ |u-\\exp(ih)|<\\epsilon. $$ The lower bound of $|h|$ could be as large as one wants. If $u\\in CU(A),$ the closure of the commutator subgroup of the unitary group, we prove that there exists a self-adjoint element $h\\in A$ such that $$ |u-\\exp(ih)| <\\epsilon and |h|\\le 2\\pi. $$ Examples are given that the bound $2\\pi$ for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0356","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"}