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

We give a new isomorphic description of the poly-Bergman spaces of the upper half-plane., and describe the C*-algebra generated by certain class of Toeplitz operators acting on each poly-Bergman space A(n)(2)(II). We consider bounded symbols depending only on theta = arg z and having limits values at theta = 0 and theta = pi. This C*-algebra is isomorphic and isometric to the C*-algebra consisting of all matrices M(x) epsilon M-n (C) circle times C[-infinity,+infinity] such that M(-infinity), M(infinity) epsilon CI. Mathematics Subject Classification. 30II20, 32A25, 47B35, 47L80.