{"paper":{"title":"Finite sections of band-dominated operators on discrete groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.OA"],"primary_cat":"math.NA","authors_text":"S. Roch, V. S. Rabinovich","submitted_at":"2010-02-23T07:11:08Z","abstract_excerpt":"Let $\\Gamma$ be a finitely generated discrete exact group. We consider operators on $l^2(\\Gamma)$ which are composed by operators of multiplication by a function in $l^\\infty (\\Gamma)$ and by the operators of left-shift by elements of $\\Gamma$. These operators generate a $C^*$-subalgebra of $L(l^2(\\Gamma))$ the elements of which we call band-dominated operators on $\\Gamma$. We study the stability of the finite sections method for band-dominated operators with respect to a given generating system of $\\Gamma$. Our approach is based on the equivalence of the stability of a sequence and the Fredho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.4258","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1002.4258/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}