Spectral theory for algebraic combinations of Toeplitzand composition operators

摘要

We determine the essential spectra of algebraic combinations of Toeplitz operators with continuoussymbol and composition operators induced by a class of linear-fractional non-automorphisms of the unitdisk. The operators in question act on the Hardy space H2 on the unit disk. Our method is to realize theC~*-algebra that they generate as an extension of the compact operators by a concrete C~*-algebra whoseinvertible elements are easily characterized.