148456 20250117162507.0 doi 10.1090/proc/15554 sideral 124447 ART-2021-124447 eng Oliva Maza, J. Universidad de Zaragoza (orcid)0000-0001-8546-5883 On lie group representations and operator ranges 2021 . In this paper, Lie group representations on Hilbert spaces are studied in relation with operator ranges. Let R be an operator range of a Hilbert space H. Given the set Λ of R-invariant operators, and given a Lie group representation ρ : G → GL(H), we discuss the induced semigroup homomorphism ρ : ρ−1(Λ) → B(R) for the operator range topology on R. In one direction, we work under the assumption ρ−1(Λ) = G, so ρ : G → B(R) is in fact a group representation. In this setting, we prove that ρ is continuous (and smooth) if and only if the tangent map dρ is R-invariant. In another direction, we prove that for the tautological representations of unitary or invertible operators of an arbitrary infinite-dimensional Hilbert space H, the set ρ−1(Λ) is neither a group for a large set of nonclosed operator ranges R nor closed for all nonclosed operator ranges R. Both results are proved by means of explicit counterexamples. info:eu-repo/grantAgreement/ES/MINECO/BES-2017-081552 info:eu-repo/grantAgreement/ES/MINECO/MTM2016-77710-P info:eu-repo/semantics/closedAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 0.971 2021 MATHEMATICS 166 / 333 = 0.498 2021 Q2 T2 MATHEMATICS, APPLIED 207 / 267 = 0.775 2021 Q4 T3 0.891 2021 Mathematics (miscellaneous) 2021 Q1 Applied Mathematics 2021 Q1 1.7 2021 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion 2006 015 Universidad de Zaragoza Dpto. Matemáticas Área Análisis Matemático 149, 10 (2021), 4317–4329 Proc. Am. Math. Soc. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 0002-9939 249378 http://zaguan.unizar.es/record/148456/files/texto_completo.pdf Postprint 1731176 http://zaguan.unizar.es/record/148456/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:148456 articulos driver 2025-01-17-14:36:09 ARTICLE