MEAN SENSITIVITY AND BANACH MEAN SENSITIVITY FOR LINEAR OPERATORS

Let(X,T)be a linear dynamical system,where X is a Banach space and T: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 sensitivi`ty and mean Li-Yorke sensitivity.