Self-Commutators of Composition Operators with Monomial Symbols on the Dirichlet Space
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 𝐶∗𝜑𝐶𝜑,𝐶𝜑𝐶∗𝜑 and self-commutators of 𝐶𝜑, which expose that t...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/618968 |