Mean sensitivity and Banach mean sensitivity for linear operators

AbstractLet (X, T) be a linear dynamical system, whereX is a Banach space andT:X→X is a bounded linear operator. This paper obtains that (X, T) is sensitive (Li-Yorke sensitive, mean sensitive, syndetically mean sensitive, respectively) if and only if (X, T) is Banach mean sensitive (Banach mean Li-Yorke sensitive, thickly multi-mean sensitive, thickly syndetically mean sensitive, respectively). Several examples are provided to distinguish between different notions of mean sensitivity, syndetic mean sensitivity and mean Li-Yorke sensitivity.

Source: European Journal of Applied Physiology - April 16, 2024 Category: Physiology Source Type: research