Dynamics of shift operators on non-metrizable sequence spaces

Abstract

[EN] We investigate dynamical properties such as topological transitivity, (sequential) hypercyclicity, and chaos for backward shift operators associated to a Schauder basis on LF-spaces. As an application, we characterize these dynamical properties for weighted generalized backward shifts on Kothe coechelon sequence spaces k(p)((v((m)))(m is an element of N)) in terms of the defining sequence of weights (v((m)))(m) (is an element of N). We further discuss several examples and show that the annihilation operator from quantum mechanics is mixing, sequentially hypercyclic, chaotic, and topologically ergodic on S'(R).