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ON THE COMMUTANT OF MULTIPLICATION OPERATORS WITH ANALYTIC POLYNOMIAL SYMBOLS

  • Robati, B. Khani (DEPARTMENT OF MATHEMATICS COLLEGE SCIENCES SHIRAZ UNIVERSITY)
  • Published : 2007.11.30

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

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