{"paper":{"title":"Symmetry and Inverse Closedness for Some Banach $^ *$-Algebras Associated to Discrete Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Marius Mantoiu","submitted_at":"2014-07-09T07:25:32Z","abstract_excerpt":"A discrete group $\\G$ is called rigidly symmetric if for every $C^*$-algebra $\\A$ the projective tensor product $\\ell^1(\\G)\\widehat\\otimes\\A$ is a symmetric Banach $^*$-algebra. For such a group we show that the twisted crossed product $\\ell^1_{\\alpha,\\o}(\\G;\\A)$ is also a symmetric Banach $^*$-algebra, for every twisted action $(\\alpha,\\o)$ of $\\G$ in a $C^*$-algebra $\\A$\\,. We extend this property to other types of decay, replacing the $\\ell^1$-condition. We also make the connection with certain classes of twisted kernels, used in a theory of integral operators involving group $2$-cocycles. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2371","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":""},"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"}