@article { author = {Abdollahi, A. and Mehrangiz, S. and Roientan, T.}, title = {Self-commutators of composition operators with monomial symbols on the Bergman space}, journal = {Bulletin of the Iranian Mathematical Society}, volume = {41}, number = {Issue 7 (Special Issue)}, pages = {65-76}, year = {2015}, publisher = {Iranian Mathematical Society (IMS)}, issn = {1017-060X}, eissn = {1735-8515}, doi = {}, 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.}, keywords = {‎‎Bergman space‎,‎composition operator‎,‎essential spectrum‎,‎essential norm‎,‎self-commutator‎}, url = {http://bims.iranjournals.ir/article_722.html}, eprint = {http://bims.iranjournals.ir/article_722_d5ce5eefb15ab5a75efe1e6a099e23e5.pdf} }