Distributionally chaotic families of operators on Fréchet spaces (Q324059)

In recent years, a systematic study of the notion of distributional chaos in the context of linear dynamics has been developed by several authors. It turns out that distributional chaos is equivalent to the existence of a distributionally irregular vector both for operators on Fréchet spaces [\textit{N. C. Bernardes jun.} et al., J. Funct. Anal. 265, No. 9, 2143--2163 (2013; Zbl 1302.47014)] and for \(C_0\)-semigroups of operators on Banach spaces [\textit{A. A. Albanese} et al., Commun. Pure Appl. Anal. 12, No. 5, 2069--2082 (2013; Zbl 1287.47007)].NEWLINENEWLINEIn the paper under review, the authors investigate the existence of distributional chaos and distributionally irregular vectors for sequences of operators between (possibly different) Fréchet spaces and for \(C_0\)-semigroups, \(\alpha\)-times integrated semigroups and \(C\)-regularized semigroups of operators on Fréchet spaces. Many previously known results are extended to these settings. Moreover, several clarifying examples and applications are also provided.