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Self‐Commutators of Composition Operators with Monomial Symbols on the Dirichlet Space

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  • A. Abdollahi
  • S. Mehrangiz

Abstract

Let φ(z) = zn, z ∈ 𝕌, for some positive integer n and Cφ the composition operator on the Dirichlet space 𝒟 induced by φ. In this paper, we completely determine the point spectrum, spectrum, essential spectrum, and essential norm of the operators Cφ∗Cφ, CφCφ∗ and self‐commutators of Cφ, which expose that the spectrum and point spectrum coincide. We also find the eigenfunctions of the operators.

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Handle: RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:618968
DOI: 10.1155/2011/618968
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