Abstract
Let Ω⊂ℂ be a simply connected domain with a piecewise smooth boundary and assume that the function F is meromorphic in\(\bar \Omega \), does not have poles on δΩ, and the index of each point λ∈ℂ\F(δΩ) with respect to the curve F(δΩ) is nonnegative (at the positive traversal of the curve δΩ). Under these assumptions, for a class of Banach spaces (including the Hardy-Smirnov spaces, the analytic spacesLip ϱ, the Bergman, Bloch spaces, etc.) one defines the Toeplitz operator TF and one establishes its similarity to the operator of multiplication f→ν·f by the projection ν of a specially selected Riemann surface б*=б*(TF called the ultraspectrum of the operator TF.
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 157, pp. 113–123, 1987.
The author is deeply grateful to his scientific advisor N. K. Nikol'skii for the formulation of the problem and for his constant interest in the paper, and also to A. A. Borichev, A. L. Vol'berg, and B. M. Solomyak for useful discussions.
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Yakubovich, D.V. Linearly similar models of Toeplitz operators. J Math Sci 44, 826–833 (1989). https://doi.org/10.1007/BF01463190
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DOI: https://doi.org/10.1007/BF01463190