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

DOI:
https://doi.org/10.1090/S0002-9939-01-05959-7

Published electronically:
March 15, 2001

MathSciNet review:
1823922

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Abstract | References | Similar Articles | Additional Information

Let be a certain Banach space consisting of continuous functions defined on the open unit disk. Let be a univalent function defined on , and assume that denotes the operator of multiplication by . We characterize the structure of the operator such that . We show that for some function in . We also characterize the commutant of under certain conditions.

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Additional Information

**B. Khani Robati**

Affiliation:
Department of Mathematics, Shiraz University, Shiraz 71454, Iran

Email:
Khani@math.susc.ac.ir

**S. M. Vaezpour**

Affiliation:
Department of Mathematics, Yazd University, Yazd, Iran

DOI:
https://doi.org/10.1090/S0002-9939-01-05959-7

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