{"paper":{"title":"Hyperrigid subsets of Cuntz-Krieger algebras and the property of rigidity at zero","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Guy Salomon","submitted_at":"2017-09-02T09:57:27Z","abstract_excerpt":"A subset $\\mathcal{G}$ generating a $C^*$-algebra $A$ is said to be hyperrigid if for every faithful nondegenerate $*$-representation $A\\subseteq B(H)$ and a sequence $\\phi_n:B(H) \\to B(H)$ of unital completely positive maps, we have that \\[ \\lim_{n\\to\\infty}\\phi_n(g)= g~~\\text{for all } g\\in \\mathcal{G} ~~ \\implies ~~ \\lim_{n\\to\\infty}\\phi_n(a)= a~~\\text{for all } a\\in A \\] where all convergence are in norm. In this paper, we show that for the Cuntz-Krieger algebra $\\mathcal{O}(G)$ associated to a row-finite directed graph $G$ with no isolated vertices, the set of partial isometries $\\mathcal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00554","kind":"arxiv","version":3},"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"}