{"paper":{"title":"Trace class groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.RT","authors_text":"Anton Deitmar, Gerrit van Dijk","submitted_at":"2015-01-10T17:46:32Z","abstract_excerpt":"A representation $\\pi$ of a locally compact group $G$ is called \\e{trace class}, if for every test function $f$ the induced operator $\\pi(f)$ is a trace class operator. The group $G$ is called \\e{trace class}, if every $\\pi\\in G$ is trace class. We show that trace class groups are type I and give a criterion for semi-direct products to be trace class and show that a representation $\\pi$ is trace class if and only if $\\pi\\otimes\\pi'$ can be realized in the space of distributions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02375","kind":"arxiv","version":5},"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"}