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C*-algebra of Angular Toeplitz Operators on Bergman Spaces over the Upper Half-plane

Commun. Math. Anal.
Volume 17, Number 2 (2014), 151 - 162

C*-algebra of Angular Toeplitz Operators on Bergman Spaces over the Upper Half-plane

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Abstract

We consider the C*-algebra generated by Toeplitz operators acting on the Bergman space over the upper half-plane whose symbols depend only on the argument of the variable. This algebra is known to be commutative, and it is isometrically isomorphic to a certain algebra of bounded complex valued functions on the real numbers. In the paper we prove that the latter algebra consists of all bounded functions f that are very slowly oscillating on the real line in the sense that the composition of f with sinh is uniformly continuous with respect to the usual metric.