Yao, Yuwu; Chen, Xiu; Zhu, Yuyang; Kang, Suling Spectral conditions of mixing \(C_0\)-semigroups on Banach spaces. (English) Zbl 1299.47086 Adv. Math., Beijing 42, No. 3, 339-347 (2013). Summary: Let \(\{T(t): t\geq 0\}\) be a \(C_0\)-semigroup on a Banach space \(X\) and \(A\) denote its infinitesimal generator. Using the point spectrum of \(A\), we give sufficient conditions for \(\{T(t): t\geq 0\}\) to be mixing or not mixing. We also characterize mixing by an admissible weight function for the translation semigroup, and employing this characterization we show that the spectral condition for \(\{T(t): t\geq 0\}\) to be mixing is not necessary. MSC: 47D06 One-parameter semigroups and linear evolution equations 47A10 Spectrum, resolvent 47D60 \(C\)-semigroups, regularized semigroups Keywords:\(C_0\)-semigroup; mixing; point spectrum; translation semigroup PDF BibTeX XML Cite \textit{Y. Yao} et al., Adv. Math., Beijing 42, No. 3, 339--347 (2013; Zbl 1299.47086)