Illinois Journal of Mathematics

Intertwining relations for Volterra operators on the Bergman space

Ce-Zhong Tong and Ze-Hua Zhou

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Abstract

On the Bergman space in the unit disk, we study the intertwining relation for Volterra type operators, whose intertwining operator is a composition operator. We also investigate the “compact” intertwining relations for Volterra type operators. As obvious consequences, the essential commutativity of Volterra type and composition operators are characterized. At the end of the paper, we find a new connection between the Bergman space and little Bloch space through this essential commutativity.

Article information

Source
Illinois J. Math., Volume 57, Number 1 (2013), 195-211.

Dates
First available in Project Euclid: 23 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1403534492

Digital Object Identifier
doi:10.1215/ijm/1403534492

Mathematical Reviews number (MathSciNet)
MR3224567

Zentralblatt MATH identifier
1311.47044

Subjects
Primary: 47B38: Operators on function spaces (general)
Secondary: 47B33: Composition operators 46E15: Banach spaces of continuous, differentiable or analytic functions 32A36: Bergman spaces

Citation

Tong, Ce-Zhong; Zhou, Ze-Hua. Intertwining relations for Volterra operators on the Bergman space. Illinois J. Math. 57 (2013), no. 1, 195--211. doi:10.1215/ijm/1403534492. https://projecteuclid.org/euclid.ijm/1403534492


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