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On bundle shifts and cluster sets

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Abstract

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.

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References

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Authors and Affiliations

  1. Instytut Matematyczny PAN, ul. Solskiego 30, 31-027, Krakow, Poland

    K. Rudol

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  1. K. Rudol
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Rudol, K. On bundle shifts and cluster sets. Integr equ oper theory 12, 444–448 (1989). https://doi.org/10.1007/BF01235743

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  • DOI: https://doi.org/10.1007/BF01235743

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