Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the commutant of operators of multiplication by univalent functions

Authors: B. Khani Robati and S. M. Vaezpour
Journal: Proc. Amer. Math. Soc. 129 (2001), 2379-2383
MSC (2000): Primary 47B35; Secondary 47B38
Published electronically: March 15, 2001
MathSciNet review: 1823922
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information


Let $\mathcal{B}$ be a certain Banach space consisting of continuous functions defined on the open unit disk. Let ${\phi}\in \mathcal{B}$ be a univalent function defined on $\overline{\mathbf{D}}$, and assume that $M_{\phi}$ denotes the operator of multiplication by ${\phi}$. We characterize the structure of the operator $T$ such that $ M_{\phi} T=T M_{\phi}$. We show that $T=M_{\varphi}$ for some function ${\varphi}$ in $\mathcal{B}$. We also characterize the commutant of $M_{{\phi}^2}$ under certain conditions.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47B35, 47B38

Retrieve articles in all journals with MSC (2000): 47B35, 47B38

Additional Information

B. Khani Robati
Affiliation: Department of Mathematics, Shiraz University, Shiraz 71454, Iran

S. M. Vaezpour
Affiliation: Department of Mathematics, Yazd University, Yazd, Iran

Keywords: Commutant, multiplication operators, Banach space of analytic functions, univalent function, bounded point evaluation
Received by editor(s): December 16, 1999
Published electronically: March 15, 2001
Additional Notes: Research of the first author was partially supported by a national grant (no. 522)
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2001 American Mathematical Society