Numerically hypercyclic polynomials

Autores UPV
Revista Archiv der Mathematik


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 $d\in \mathbb{N}$. Moreover, if $X$ is infinite-dimensional, then one can find hypercyclic non-homogeneous polynomials of arbitrary degree which are at the same time numerically hypercyclic. We prove that weighted shift polynomials cannot be numerically hypercyclic neither on $c_0$ nor on $\ell_p$ for $1 \leq p < \infty$. In contrast, we characterize numerically hypercyclic weighted shift polynomials on $\ell_\infty$.