Niknam, A.; Assadi, A. On semigroups of linear operators. (English) Zbl 1084.46529 Commun. Appl. Anal. 4, No. 4, 449-452 (2000). Summary: In this note we discuss some groups of linear operators on \(C^*\)-algebras and their infinitesimal generators. We show that if \(\delta\) is the infinitesimal generator of a strongly countinuous one-parameter group of automorphisms \(\{\alpha_t\}_{t\in\mathbb{R}}\) such that \(\delta\) is approximately inner in a core for \(\delta\), then \(\{\alpha_t\}_{t\in\mathbb{R}}\) is approximately inner. We also prove that the infinitesimal generator of some strongly continuous automorphism groups of \(C^*\)-subalgebras of operators is strongly approximately inner on some dense subset of a Hilbert space. MSC: 46L05 General theory of \(C^*\)-algebras 46L57 Derivations, dissipations and positive semigroups in \(C^*\)-algebras 47D03 Groups and semigroups of linear operators 47D06 One-parameter semigroups and linear evolution equations 47L45 Dual algebras; weakly closed singly generated operator algebras 47B47 Commutators, derivations, elementary operators, etc. PDFBibTeX XMLCite \textit{A. Niknam} and \textit{A. Assadi}, Commun. Appl. Anal. 4, No. 4, 449--452 (2000; Zbl 1084.46529)