Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 8, Number 3 (2017), 366-376.
The commutant of a multiplication operator with a finite Blaschke product symbol on the Sobolev disk algebra
Let be the algebra generated in the Sobolev space by the rational functions with poles outside the unit disk . This is called the Sobolev disk algebra. In this article, the commutant of the multiplication operator on is studied, where is an n-Blaschke product. We prove that an operator is in if and only if , where , and is given by , , .
Ann. Funct. Anal., Volume 8, Number 3 (2017), 366-376.
Received: 2 June 2016
Accepted: 29 October 2016
First available in Project Euclid: 22 April 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 47B38: Operators on function spaces (general)
Secondary: 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.) 46E20: Hilbert spaces of continuous, differentiable or analytic functions
Zhao, Ruifang; Wang, Zongyao; Larson, David R. The commutant of a multiplication operator with a finite Blaschke product symbol on the Sobolev disk algebra. Ann. Funct. Anal. 8 (2017), no. 3, 366--376. doi:10.1215/20088752-2017-0002. https://projecteuclid.org/euclid.afa/1492826603