Syndetic Sensitivity and Mean Sensitivity for Linear Operators

Abstract

We study syndetic sensitivity and mean sensitivity for linear dynamical systems. For the syndetic sensitivity aspect, we obtain some properties of syndetic sensitivity for adjoint operators and left multiplication operators. We also show that there exists a linear dynamical system (X×Y,T×S) such that (X×Y,T×S) is cofinitely sensitive but (X,T) and (Y,S) are not syndetically sensitive. For the mean sensitivity aspect, we show that if (Y,S) is sensitive and not mean sensitive, where Y is a complex Banach space, the spectrum of T meets the unit circle. We also obtain some results regarding mean sensitive perturbations.