Commutants of analytic Toeplitz operators on the Bergman space

In this note we show that if two Toeplitz operators on a Bergman space commute and the symbol of one of them is analytic and nonconstant, then the other one is also analytic.

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2000-07, Vol.128 (7), p.1951-1953
Main Authors: Axler, Sheldon, Čučković, Željko, Rao, N. V.
Format: Article
Language:English
Subjects:
Algebra
Analytic functions
Approximation
Harmonic functions
Mathematical constants
Mathematical functions
Mathematical theorems
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Description
Summary:In this note we show that if two Toeplitz operators on a Bergman space commute and the symbol of one of them is analytic and nonconstant, then the other one is also analytic.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-99-05436-2