ON THE COMMUTANT OF MULTIPLICATION OPERATORS WITH ANALYTIC POLYNOMIAL SYMBOLS

Title & Authors
ON THE COMMUTANT OF MULTIPLICATION OPERATORS WITH ANALYTIC POLYNOMIAL SYMBOLS
Robati, B. Khani;

Abstract
Let $\small{\mathcal{B}}$ be a certain Banach space consisting of analytic functions defined on a bounded domain G in the complex plane. Let $\small{{\varphi}}$ be an analytic polynomial or a rational function and let $\small{M_{\varphi}}$ denote the operator of multiplication by $\small{{\varphi}}$. Under certain condition on $\small{{\varphi}}$ and G, we characterize the commutant of $\small{M_{\varphi}}$ that is the set of all bounded operators T such that $\small{TM_{\varphi}=M_{\varphi}T}$. We show that $\small{T=M_{\Psi}}$, for some function $\small{{\Psi}}$ in $\small{\mathcal{B}}$.
Keywords
commutant;multiplication operators;Banach space of analytic functions;univalent function;bounded point evaluation;
Language
English
Cited by
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