Abstract and Applied Analysis

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

Zhong-Shan Fang and Ze-Hua Zhou

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Abstract

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

Permanent link to this document
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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