{"paper":{"title":"Matrix coefficients of unitary representations and associated compactifications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Nico Spronk, Ross Stokke","submitted_at":"2011-12-20T23:14:41Z","abstract_excerpt":"We study, for a locally compact group $G$, the compactifications $(\\pi,G^\\pi)$ associated with unitary representations $\\pi$, which we call {\\it $\\pi$-Eberlein compactifications}. We also study the Gelfand spectra $\\Phi_{\\mathcal{A}}(\\pi)}$ of the uniformly closed algebras $\\mathcal{A}(\\pi)$ generated by matrix coefficients of such $\\pi$. We note that $\\Phi_{\\mathcal{A}(\\pi)}\\cup\\{0\\}$ is itself a semigroup and show that the \\v{S}ilov boundary of $\\mathcal{A}(\\pi)$ is $G^\\pi$. We study containment relations of various uniformly closed algebras generated by matrix coefficients, and give a new c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4878","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"}