Discrete-time theorems for the dichotomy of one-parameter semigroups
Continuing investigations of \textit{P. Preda} and \textit{M. Megan} [Bull.\ Austral.\ Math.\ Soc. 30, 435--448 (1984; Zbl 0547.47022)], the author gives several discrete-time sufficient conditions for the dichotomy of a \(C_0\)-semigroup \(T(t)_{t\geq0}\) on a Banach space in the general case when it is not required that the kernel of the dichotomic projector is \(T(t)\)-invariant. Complete characterizations for the exponential dichotomy are also given with the additional requirement that the dichotomic projector commutes with \(T(t)\) for each \(t\geq0\).
scientific article; zbMATH DE number 5289870