{"paper":{"title":"On an invariance property of the space of smooth vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.RT","authors_text":"Christoph Zellner, Hadi Salmasian, Karl-Hermann Neeb","submitted_at":"2014-01-14T05:31:05Z","abstract_excerpt":"Let $(\\pi, \\mathcal H)$ be a continuous unitary representation of the (infinite dimensional) Lie group $G$ and $\\gamma \\: \\mathbb R \\to \\mathrm{Aut}(G)$ define a continuous action of $\\mathbb R$ on $G$. Suppose that $\\pi^\\#(g,t) = \\pi(g) U_t$ defines a continuous unitary representation of the semidirect product group $G \\rtimes_\\gamma \\mathbb R$. The first main theorem of the present note provides criteria for the invariance of the space $\\mathcal H^\\infty$ of smooth vectors of $\\pi$ under the operators $U_f = \\int_\\mathbb R f(t)U_t\\, dt$ for $f \\in L^1(\\mathbb R)$, resp., $f \\in \\mathcal S(\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3072","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"}