A note on topological and strict transitivity

Abstract

AbstractLet X be a normed linear space and L(X) be the algebra of continuous linear operators on X. We give a necessary condition for topological transitivity of subsets of L(X) which gives a necessary condition for hypercyclicity and supercyclicity of a single operator on X. Also, We prove the strict transitivity of some particular families of operators on locally convex spaces and Hilbert spaces.Key words and phrases: hypercyclic, supercyclic, topologically transitive, strictly transitive