Hypercyclic operators on algebra of symmetric analytic functions on $\ell_p$

Z.G. Mozhyrovska

doi:10.15330/cmp.8.1.127-133

Hypercyclic operators on algebra of symmetric analytic functions on $\ell_p$

Authors

Z.G. Mozhyrovska Lviv University of Trade and Economics, 10 Tuhan-Baranovskyi str., 79005, Lviv, Ukraine https://orcid.org/0000-0003-2283-1879

https://doi.org/10.15330/cmp.8.1.127-133

Keywords:

hypercyclic operators, functional spaces, symmetric functions

Published online: 2016-06-30

Abstract

In the paper, it is proposed a method of construction of hypercyclic composition operators on $H(\mathbb{C}^n)$ using polynomial automorphisms of $\mathbb{C}^n$ and symmetric analytic functions on $\ell_p.$ In particular, we show that an "symmetric translation" operator is hypercyclic on a Frechet algebra of symmetric entire functions on $\ell_p$ which are bounded on bounded subsets.