Illinois Journal of Mathematics

Common bounded universal functions for composition operators

Frédéric Bayart, Sophie Grivaux, and Raymond Mortini

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Abstract

Let $\mathcal{A}$ be the set of automorphisms of the unit disk with $1$ as attractive fixed point. We prove that there exists a single Blaschke product that is universal for every composition operator $C_\phi$, $\phi\in\mathcal{A}$, acting on the unit ball of $H^\infty(\mathbb{D})$.

Article information

Source
Illinois J. Math., Volume 52, Number 3 (2008), 995-1006.

Dates
First available in Project Euclid: 1 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1254403727

Digital Object Identifier
doi:10.1215/ijm/1254403727

Mathematical Reviews number (MathSciNet)
MR2546020

Zentralblatt MATH identifier
1181.47019

Subjects
Primary: 47A16: Cyclic vectors, hypercyclic and chaotic operators 47B33: Composition operators

Citation

Bayart, Frédéric; Grivaux, Sophie; Mortini, Raymond. Common bounded universal functions for composition operators. Illinois J. Math. 52 (2008), no. 3, 995--1006. doi:10.1215/ijm/1254403727. https://projecteuclid.org/euclid.ijm/1254403727


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