## Abstract and Applied Analysis

### Differences of Composition Operators on the Space of Bounded Analytic Functions in the Polydisc

#### Abstract

This paper gives some estimates of the essential norm for the difference of composition operators induced by $\varphi$ and $\psi$ acting on the space, ${H}^{\infty }({\mathbb{D}}^{n})$, of bounded analytic functions on the unit polydisc ${\mathbb{D}}^{n}$, where $\varphi$ and $\psi$ are holomorphic self-maps of ${\mathbb{D}}^{n}$. As a consequence, one obtains conditions in terms of the Carathéodory distance on ${\mathbb{D}}^{n}$ that characterizes those pairs of holomorphic self-maps of the polydisc for which the difference of two composition operators on ${H}^{\infty }({\mathbb{D}}^{n})$ is compact.

#### Article information

Source
Abstr. Appl. Anal., Volume 2008 (2008), Article ID 983132, 10 pages.

Dates
First available in Project Euclid: 10 February 2009

https://projecteuclid.org/euclid.aaa/1234299000

Digital Object Identifier
doi:10.1155/2008/983132

Mathematical Reviews number (MathSciNet)
MR2466222

Zentralblatt MATH identifier
1160.32009

#### Citation

Fang, Zhong-Shan; Zhou, Ze-Hua. Differences of Composition Operators on the Space of Bounded Analytic Functions in the Polydisc. Abstr. Appl. Anal. 2008 (2008), Article ID 983132, 10 pages. doi:10.1155/2008/983132. https://projecteuclid.org/euclid.aaa/1234299000

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