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

Z. G. Mozhyrovska

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.


Keywords


hypercyclic operators, functional spaces, symmetric functions

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