Karpatsʹkì Matematičnì Publìkacìï (Jun 2016)

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

  • Z.G. Mozhyrovska

DOI
https://doi.org/10.15330/cmp.8.1.127-133
Journal volume & issue
Vol. 8, no. 1
pp. 127 – 133

Abstract

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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.

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