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# Hypercyclic composition operators on Hilbert spaces of analytic functions

### Abstract

In the paper we consider composition operators on Hilbert spaces of analytic functions of infinitely many variables. In particular, we establish some conditions under which composition operators are hypercyclic and construct some examples of Hilbert spaces of analytic functions which do not admit hypercyclic operators of composition with linear operators.

Key words: Hypercyclic operators, composition operators, Hilbert space of analytic functions.

### Article Information

 Title Hypercyclic composition operators on Hilbert spaces of analytic functions Source Methods Funct. Anal. Topology, Vol. 20 (2014), no. 3, 284-291 MathSciNet MR3242709 zbMATH 1324.47017 Milestones Received 28/11/2012; Revised 28/04/2014 Copyright The Author(s) 2014 (CC BY-SA)

### Authors Information

Z. H. Mozhyrovska
Lviv Commercial Academy, 10 Tuhan-Baranovsky Str., Lviv, 79005, Ukraine

A. V. Zagorodnyuk
Vasyl Stefanyk Prykarpatskyi National University, 57 Shevchenka Str., Ivano-Frankivsk, 76000, Ukraine

### Citation Example

Z. H. Mozhyrovska and A. V. Zagorodnyuk, Hypercyclic composition operators on Hilbert spaces of analytic functions, Methods Funct. Anal. Topology 20 (2014), no. 3, 284-291.

### BibTex

@article {MFAT673,
AUTHOR = {Mozhyrovska, Z. H. and Zagorodnyuk, A. V.},
TITLE = {Hypercyclic composition operators on Hilbert spaces of analytic functions},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {20},
YEAR = {2014},
NUMBER = {3},
PAGES = {284-291},
ISSN = {1029-3531},
MRNUMBER = {MR3242709},
ZBLNUMBER = {1324.47017},
URL = {http://mfat.imath.kiev.ua/article/?id=673},
}