an:06310591
Zbl 1299.47086
Yao, Yuwu; Chen, Xiu; Zhu, Yuyang; Kang, Suling
Spectral conditions of mixing \(C_0\)-semigroups on Banach spaces
EN
Adv. Math., Beijing 42, No. 3, 339-347 (2013).
00333706
2013
j
47D06 47A10 47D60
\(C_0\)-semigroup; mixing; point spectrum; translation semigroup
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.