RT journal article
T1 Supercyclicity of weighted composition operators on spaces of continuous functions
A1 Beltrán-Meneu, M.J.
A1 Jordá, E.
A1 Murillo Arcila, Marina
A2 Matemáticas
K1 Weighted composition operator
K1 Weak supercyclicity
K1 Disc algebra
K1 Space of holomorphic functions
AB 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.
PB Springer
SN 0010-0757
YR 2020
FD 2020
LK http://hdl.handle.net/10498/35374
UL http://hdl.handle.net/10498/35374
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 11-nov-2026