Albanese, Angela Ama; Bonet Solves, José Antonio; Ricker, Werner J.(Elsevier, 2013-05-01)
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, ...
Bès, Juan P.; Martin, Özgür; Peris Manguillot, Alfredo; Shkarin, Stanislav A.(Elsevier, 2012-09-01)
Chan and Shapiro showed that each (non-trivial) translation operator f(z){mapping} Tλf(z+λ) acting on the Fréchet space of entire functions endowed with the topology of locally uniform convergence supports a universal ...
In this paper, we show that every complex Banach space X with dimension at least 2 supports a numerically hypercyclic d-homogeneous polynomial P for every . Moreover, if X is infinite-dimensional, then one can find hypercyclic ...
We establish a general result on the existence of hypercyclic (resp., transitive, weakly mixing, mixing, frequently hypercyclic) polynomials on locally convex spaces. As a consequence we prove that every (real or complex) ...