1
Department of Mathematics, Shiraz University, Shiraz, Iran.
2
Department of Engineering, Khonj Branch, Islamic Azad University, Khonj, Iran.
Abstract
Let $\varphi(z)=z^m, z \in \mathbb{U}$, for some positive integer $m$, and $C_\varphi$ be the composition operator on the Bergman space $\mathcal{A}^2$ induced by $\varphi$. In this article, we completely determine the point spectrum, spectrum, essential spectrum, and essential norm of the operators $C^*_\varphi C_\varphi, C_\varphi C^*_\varphi$ as well as self-commutator and anti-self-commutators of $C_\varphi$. We also find the eigenfunctions of these operators.
Abdollahi, A., Mehrangiz, S., & Roientan, T. (2015). Self-commutators of composition operators with monomial symbols on the Bergman space. Bulletin of the Iranian Mathematical Society, 41(Issue 7 (Special Issue)), 65-76.
MLA
A. Abdollahi; S. Mehrangiz; T. Roientan. "Self-commutators of composition operators with monomial symbols on the Bergman space". Bulletin of the Iranian Mathematical Society, 41, Issue 7 (Special Issue), 2015, 65-76.
HARVARD
Abdollahi, A., Mehrangiz, S., Roientan, T. (2015). 'Self-commutators of composition operators with monomial symbols on the Bergman space', Bulletin of the Iranian Mathematical Society, 41(Issue 7 (Special Issue)), pp. 65-76.
VANCOUVER
Abdollahi, A., Mehrangiz, S., Roientan, T. Self-commutators of composition operators with monomial symbols on the Bergman space. Bulletin of the Iranian Mathematical Society, 2015; 41(Issue 7 (Special Issue)): 65-76.
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