{"paper":{"title":"F{\\o}lner sequences in operator theory and operator algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.OA","authors_text":"Dmitry V. Yakubovich, Fernando Lled\\'o, Pere Ara","submitted_at":"2013-03-14T10:20:32Z","abstract_excerpt":"The present article is a review of recent developments concerning the notion of F{\\o}lner sequences both in operator theory and operator algebras. We also give a new direct proof that any essentially normal operator has an increasing F{\\o}lner sequence $\\{P_n\\}$ of non-zero finite rank projections that strongly converges to 1. The proof is based on Brown-Douglas-Fillmore theory. We use F{\\o}lner sequences to analyze the class of finite operators introduced by Williams in 1970. In the second part of this article we examine a procedure of approximating any amenable trace on a unital and separabl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3392","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"}