ℱ -Sensitivity for Linear Dynamics and Its Induced Hyperspace Dynamics

In this paper we study ℱ -sensitivity for a bounded linear operator T on Banach space and its induced hyperspace dynamics. First, we suggest the necessary and sufficient condition for ℱ -sensitivity for a bounded linear operator T on Banach space. Next, we consider the natural hyperspace extensions T and T̃ of T to the space K(X) of compact subsets of X and C(X) of convex compact subsets of X, respectively. We show that ℱ -sensitivity is equivalent for the maps T, T and T̃ .