Orbital and spectral aspects of hypercyclic operators and semigroups

Abstract

In connection with the theory of hypercyclicity of bounded linear operators and strongly continuous semigroups of operators on Banach spaces, we make several observations about the following three topics – (i) special types of orbits, (ii) the role of large subsets of N, (iii) various spectral conditions – and thereby highlight some nuances of the theory.