Resumen de Dynamics of shift operators on non-metrizable sequence spaces

José Antonio Bonet Solves , Thomas Kalmes , Alfredo Peris

• 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 Köthe coechelon sequence spaces kp((v(m))m∈N) in terms of the defining sequence of weights (v(m))m∈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).