THE C*-ALGEBRA GENERATED BY IRREDUCIBLE TOEPLITZ AND COMPOSITION OPERATORS

摘要

We describe the C*-algebra generated by an irreducible Toeplitz operator T-psi, with continuous symbol psi on the unit circle T, and finitely many composition operators on the Hardy space H-2 induced by certain linear-fractional self-maps of the unit disc, modulo the ideal of compact operators K(H-2). For composition operators with automorphism symbols, we show that this algebra is not isomorphic to the one generated by the shift and composition operators.