×

zbMATH — the first resource for mathematics

Spectral conditions of mixing \(C_0\)-semigroups on Banach spaces. (English) Zbl 1299.47086
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
PDF BibTeX XML Cite