%0 Journal Article 
%A Beltrán-Meneu, M.J.
%A Jordá, E.
%A Murillo Arcila, Marina
%T Supercyclicity of weighted composition operators on spaces of continuous functions
%D 2020
%@ 0010-0757
%U http://hdl.handle.net/10498/35374
%X Our study is focused on the dynamics of weighted composition operators  defined on a locally convex space $E\hookrightarrow (C(X),\tau_p)$  with $X$ being a topological  Hausdorff space containing at least two different points and such that the evaluations $\{\delta_x:\ x\in X\}$ are linearly independent in $E'$.  We prove, when $X$ is compact and $E$ is a Banach space  containing a nowhere vanishing function, that a weighted composition operator $\W$ is never weakly supercyclic on $E$. 
We also prove that if the symbol $\varphi$ lies  in the unit ball of $A(\D)$, then every weighted composition operator can never be $\tau_p$-supercyclic neither on  $C(\D)$ nor on the disc algebra $A(\D)$.
Finally,  we obtain  Ansari-Bourdon type  results and conditions on the spectrum for arbitrary weakly supercyclic operators, and we provide necessary conditions for a composition operator to be weakly supercyclic on the space of holomorphic functions defined in non necessarily simply connected planar domains. As a consequence, we show that no composition operator can be weakly supercyclic neither on the space of holomorphic functions on the punctured disc nor in the punctured plane.
%K Weighted composition operator
%K Weak supercyclicity
%K Disc algebra
%K Space of holomorphic functions
%~ Universidad de Cádiz