[EN] We characterize Köthe echelon spaces (and, more generally, those Fréchet spaces with an unconditional basis) which are Schwartz, in terms of the convergence of the Cesàro means of power bounded operators defined on ...

Every Köthe echelon Fréchet space XX that is Montel and not isomorphic to a countable product of copies of the scalar field admits a power bounded continuous linear operator TT such that I−TI−T does not have closed range, ...

[EN] In this paper we consider composition operators on locally convex spaces of functions defined on R. We prove results concerning supercyclicity, power boundedness, mean ergodicity and convergence of the iterates in the ...

[EN] The composition operators defined on little Bloch spaces, Bergman spaces, Hardy spaces or little weighted Bergman spaces of infinite type, when well defined, are shown to be mean ergodic if and only if they are power ...

[EN] Necessary and sufficient conditions are given for mean ergodicity, power boundedness, and topologizability for weighted backward shift and weighted forward shift operators, respectively, on Kothe echelon spaces in ...

We study the dynamical behaviour of composition operators defined on spaces of real analytic functions. We characterize when such operators are power bounded, i.e. when the orbits of all the elements are bounded. In this ...