{"paper":{"title":"Group representations with empty residual spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Yemon Choi","submitted_at":"2009-06-16T19:40:48Z","abstract_excerpt":"Let $X$ be a Banach space on which a discrete group $\\Gamma$ acts by isometries. For certain natural choices of $X$, every element of the group algebra, when regarded as an operator on $X$, has empty residual spectrum. We show, for instance, that this occurs if $X$ is $\\ell^2(\\Gm)$ or the group von Neumann algebra $VN(\\Gm)$. In our approach, we introduce the notion of a {\\em surjunctive pair}, and develop some of the basic properties of this construction.\n  The cases $X=\\ell^p(\\Gm)$ for $1<p<2$ or $2<p<\\infty$ are more difficult. If $\\Gm$ is amenable we can obtain partial results, using a majo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.2854","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"}