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  

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd