{"paper":{"title":"Convolution dominated operators on compact extensions of abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Gero Fendler, Michael Leinert","submitted_at":"2017-11-23T10:13:37Z","abstract_excerpt":"If $G$ is a locally compact group, $CD(G)$ the algebra of convolution dominated operators on $L^2(G)$ then an important question is: Is $\\mathbb{C}1+CD(G)$ (respectively $CD(G)$ if $G$ is discrete) inverse-closed in the bounded operators on $L^2(G)$? In this note we answer this question in the affirmative provided $G$ is such that one of the following properties is fulfilled (1) There is a discrete, rigidly symmetric, and amenable subgroup $H\\subset G$ and a (measurable) relatively compact neighbourhood of the identity $U$ invariant under conjugation by elements of $H$ such that $\\{hU\\;:\\;h\\in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08638","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"}