C*-algebra generated by angular toeplitz operators on the weighted bergman spaces over the upper half-plane

We consider the set of all Toeplitz operators acting on the weighted Bergman space over the upper half-plane whose L_∞-symbols depend only on the argument of the polar coordinates. The main result states that the uniform closure of this set coincides with the C^∗-algebra generated by the above Toeplitz operators and is isometrically isomorphic to the C^∗-algebra of bounded functions that are very slowly oscillating on the real line in the sense that they are uniformly continuous with respect to the arcsinh-metric on the real line.