%0 Journal Article %T Self-commutators of composition operators with monomial symbols on the Bergman space %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Abdollahi, A. %A Mehrangiz, S. %A Roientan, T. %D 2015 %\ 12/01/2015 %V 41 %N Issue 7 (Special Issue) %P 65-76 %! Self-commutators of composition operators with monomial symbols on the Bergman space %K ‎‎Bergman space‎ %K ‎composition operator‎ %K ‎essential spectrum‎ %K ‎essential norm‎ %K ‎self-commutator‎ %R %X 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. %U http://bims.iranjournals.ir/article_722_d5ce5eefb15ab5a75efe1e6a099e23e5.pdf