Toeplitz Operators with Vertical Symbols Acting on the Poly-Bergman Spaces of the Upper Half-Plane

摘要

We describe the C*-algebra generated by the Toeplitz operators acting on each poly-Bergman space of the upper half-plane Pi subset of C . We consider bounded symbols depending only on y = Im z and having limit values at y = 0 and y = infinity. This C* algebra is isomorphic to the C*-algebra of all matrices of dimension n x n whose entries are continuous functions over the positive reals, and are scalar multiples of the identity matrix at y = 0 and y = infinity.