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

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  • Zhong-Shan Fang
  • Ze-Hua Zhou

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∞(Dn), of bounded analytic functions on the unit polydisc Dn, where φ and ψ are holomorphic self‐maps of Dn. As a consequence, one obtains conditions in terms of the Carathéodory distance on Dn that characterizes those pairs of holomorphic self‐maps of the polydisc for which the difference of two composition operators on H∞(Dn) is compact.

Suggested Citation

  • Zhong-Shan Fang & Ze-Hua Zhou, 2008. "Differences of Composition Operators on the Space of Bounded Analytic Functions in the Polydisc," Abstract and Applied Analysis, John Wiley & Sons, vol. 2008(1).
    • Handle: RePEc:wly:jnlaaa:v:2008:y:2008:i:1:n:983132
    DOI: 10.1155/2008/983132
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    References listed on IDEAS

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    1. Sei-Ichiro Ueki & Luo Luo, 2008. "Compact Weighted Composition Operators and Multiplication Operators between Hardy Spaces," Abstract and Applied Analysis, Hindawi, vol. 2008, pages 1-12, March.
    2. Sei-Ichiro Ueki & Luo Luo, 2008. "Compact Weighted Composition Operators and Multiplication Operators between Hardy Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2008(1).
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    Cited by:

    1. M. Haji Shaabani & B. Khani Robati, 2009. "On the Norm of Certain Weighted Composition Operators on the Hardy Space," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).

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