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On bundle shifts and cluster sets. (English) Zbl 0685.47024
Using some results of K. Rudol and of M. B. Abrahamse, R. G. Douglas on subnormal operators, the author shows a wide class of analytic Toeplitz operators are unitarily equivalent to bundle shifts. The author studies also the essential spectrum of these operators.
Reviewer: Bui Doan Khanh
MSC:
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
47B20 Subnormal operators, hyponormal operators, etc.
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[1] M. B. Abrahamse, R. G. Douglas. A class of subnormal operators related to multiply connected domains,Adv. in Math. 19 (1976), 106-148 · Zbl 0321.47019 · doi:10.1016/0001-8708(76)90023-2
[2] M. B. Abrahamse, T. Kriete, The spectral multiplicity of a multiplication operator.Ind. Univ. Math. J. 22 (1973), 845-857 · Zbl 0259.47031 · doi:10.1512/iumj.1973.22.22072
[3] E. Collingwood, A. Lohwater, The Theory of Cluster Sets.Cambridge Univ. Press 1966 · Zbl 0149.03003
[4] J. B. Conway, Spectral properties of certain operators on Hardy spaces of planar domains.Integral Eqs. Op. Theory 10 (1987), 659-706 · Zbl 0658.47028 · doi:10.1007/BF01195796
[5] J. A. Deddens, Analytic Toeplitz and composition operators,Canad. Math. J. 24 (1972), 859-865. · Zbl 0273.47016 · doi:10.4153/CJM-1972-085-8
[6] K. Rudol, Spectral mapping theorems for analytic functional calculi, Op. Theory: Adv. Appl.17, pp. 331-340,Birkhäuser Verl. 1986
[7] K. Rudol, The generalised Wold Decomposition for subnormal operators,Integral Eqs. Op. Theory 11 (1988), 420-436. · Zbl 0645.47021 · doi:10.1007/BF01202080
[8] Yang Liming, Equality of essential spectra of quasisimilar subnormal operators,Scientia Sinica (to appear) · Zbl 0664.47015
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