{"paper":{"title":"Analytic extension techniques for unitary representations of Banach-Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.RT","authors_text":"Karl-Hermann Neeb, St\\'ephane Merigon","submitted_at":"2011-02-01T16:49:25Z","abstract_excerpt":"Let $(G,\\theta)$ be a Banach--Lie group with involutive automorphism $\\theta$, $\\g = \\fh \\oplus \\fq$ be the $\\theta$-eigenspaces in the Lie algebra $\\g$ of $G$, and $H = (G^\\theta)_0$ be the identity component of its group of fixed points. An Olshanski semigroup is a semigroup $S \\subeq G$ of the form $S = H \\exp(W)$, where $W$ is an open $\\Ad(H)$-invariant convex cone in $\\fq$ and the polar map $H \\times W \\to S, (h,x) \\mapsto h \\exp x$ is a diffeomorphism. Any such semigroup carries an involution * satisfying $(h\\exp x)^* = (\\exp x) h^{-1}$. Our central result, generalizing the L\\\"uscher--Ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0213","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"}