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http://dx.doi.org/10.4134/BKMS.2007.44.4.683

ON THE COMMUTANT OF MULTIPLICATION OPERATORS WITH ANALYTIC POLYNOMIAL SYMBOLS

Robati, B. Khani (DEPARTMENT OF MATHEMATICS COLLEGE SCIENCES SHIRAZ UNIVERSITY)

Publication Information

Bulletin of the Korean Mathematical Society / v.44, no.4, 2007 , pp. 683-689 More about this Journal

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;

Citations & Related Records

Times Cited By Web Of Science : 0 (Related Records In Web of Science)
Times Cited By SCOPUS : 1

Reference
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