TY - JOUR ID - 722 TI - Self-commutators of composition operators with monomial symbols on the Bergman space JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Abdollahi, A. AU - Mehrangiz, S. AU - Roientan, T. AD - Department of Mathematics, Shiraz University, Shiraz, Iran. AD - Department of Engineering, Khonj Branch, Islamic Azad University, Khonj, Iran. Y1 - 2015 PY - 2015 VL - 41 IS - Issue 7 (Special Issue) SP - 65 EP - 76 KW - ‎‎Bergman space‎ KW - ‎composition operator‎ KW - ‎essential spectrum‎ KW - ‎essential norm‎ KW - ‎self-commutator‎ DO - N2 - 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. UR - http://bims.iranjournals.ir/article_722.html L1 - http://bims.iranjournals.ir/article_722_d5ce5eefb15ab5a75efe1e6a099e23e5.pdf ER -