On bundle shifts and cluster sets

An application of the Abrahamse-Douglas model of subnormal operators ([1], [7]) to the theory of analytic functions is presented. Section 1 shows a wide class of analytic Toeplitz operators covered by the model, i. e. equivalent to bundle shifts. In Section 2 their essential spectra are considered. As corollaries, we get the equality of essential spectra of certain quasisimilar Toeplitz operators and a nice property of global (boundary) cluster sets. Section 3, entitledApology points out two inexact claims made in the introductory part of [7]. Fortunately, none of the results was affected by these errors.