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 On the commutant of multiplication operators with analytic polynomial symbols Bull. Korean Math. Soc. 2007 Vol. 44, No. 4, 683-689 Published online December 1, 2007 B. Khani Robati Shiraz University Abstract : Let ${\mathcal B}$ be a certain Banach space consisting of analytic functions defined on a bounded domain $G$ in the complex plane. Let $\varphi$ be an analytic polynomial or a rational function and let $M_{\varphi}$ denote the operator of multiplication by $\varphi$. Under certain condition on $\varphi$ and $G$, we characterize the commutant of $M_{\varphi}$ that is the set of all bounded operators $T$ such that $TM_{\varphi}=M_{\varphi}T$. We show that $T=M_{\Psi}$ for some function $\Psi$ in ${\mathcal B}$. Keywords : commutant, multiplication operators, Banach space of analytic functions, univalent function, bounded point evaluation. MSC numbers : Primary 47B35; Secondary 47B38 Downloads: Full-text PDF