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

A. Abdollahi and S. Mehrangiz

Abstract and Applied Analysis, 2011, vol. 2011, 1-9

Abstract:

Let 𠜑 ( 𠑧 ) = 𠑧 ð ‘› , 𠑧 ∈ ð •Œ , for some positive integer ð ‘› and ð ¶ ð œ‘ the composition operator on the Dirichlet space ð ’Ÿ induced by 𠜑 . In this paper, we completely determine the point spectrum, spectrum, essential spectrum, and essential norm of the operators ð ¶ âˆ— 𠜑 ð ¶ ð œ‘ , ð ¶ ð œ‘ ð ¶ âˆ— 𠜑 and self-commutators of ð ¶ ð œ‘ , which expose that the spectrum and point spectrum coincide. We also find the eigenfunctions of the operators.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:618968

DOI: 10.1155/2011/618968

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