The question of whether a hypercyclic operator T acting on Fréchet algebra X admits or not an vectors (but 0) has been addressed in the recent literature. In this paper we give new criteria and characterisations context convolution operators H(C) backward shifts general sequence algebra. Analogous questions arise for stronger properties like frequent hypercyclicity. trend sufficient condition w...

In this paper we characterize hypercyclic sequences of weighted translation operators on an Orlicz space in the context locally compact hypergroups.

In this paper we introduce and study the notion of hypercyclicity for iterated function systems (IFS) operators. We prove that a linear IFS, implies sensitivity if an IFS is abelian, then also multi-sensitivity hence thick sensitivity. give some equivalent conditions as well weakly mixing

We prove that, given a sequence of points in a complex domain Ω without accumulation points, there are functions having prescribed values at the points of the sequence and, simultaneously, having dense orbit in the space of holomorphic functions on Ω . The orbit is taken with respect to any fixed nonscalar differential operator generated by an entire function of subexponential type, thereby ext...

We study hypercyclicity of Toeplitz operators in the Hardy space H2(D) with symbols form R(z‾)+φ(z), where R is a rational function and φ∈H∞(D). relate this problem to cyclicity certain families functions for analytic give new sufficient conditions based on deep results B. Solomyak.