{"paper":{"title":"On the characterization of trace class representations and Schwartz operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Christoph Zellner, Gerrit van Dijk, Hadi Salmasian, Karl-Hermann Neeb","submitted_at":"2015-12-08T13:12:48Z","abstract_excerpt":"In this note we collect several characterizations of unitary representations $(\\pi, \\mathcal{H})$ of a finite dimensional Lie group $G$ which are trace class, i.e., for each compactly supported smooth function $f$ on $G$, the operator $\\pi(f)$ is trace class. In particular we derive the new result that, for some $m \\in \\mathbb{N}$, all operators $\\pi(f)$, $f \\in C^m_c(G)$, are trace class. As a consequence the corresponding distribution character $\\theta_\\pi$ is of finite order. We further show $\\pi$ is trace class if and only if every operator $A$, which is smoothing in the sense that $A\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02451","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"}