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Banach algebra generated by a finite number of bergman polykernel operators, continuous coefficients, and a finite group of shifts

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Ukrainian Mathematical Journal Aims and scope

We study the Banach algebra generated by a finite number of Bergman polykernel operators with continuous coefficients that is extended by operators of weighted shift that form a finite group. By using an isometric transformation, we represent the operators of the algebra in the form of a matrix operator formed by a finite number of mutually complementary projectors whose coefficients are Toeplitz matrix functions of finite order. Using properties of Bergman polykernel operators, we obtain an efficient criterion for the operators of the algebra considered to be Fredholm operators.

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Authors and Affiliations

  1. Hydroacoustics Division of the Marine Hydrophysical Institute, Ukrainian National Academy of Sciences, Odessa, Ukraine

    V. A. Mozel’

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  1. V. A. Mozel’
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 9, pp. 1247–1255, September, 2010.

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Mozel’, V.A. Banach algebra generated by a finite number of bergman polykernel operators, continuous coefficients, and a finite group of shifts. Ukr Math J 62, 1449–1459 (2011). https://doi.org/10.1007/s11253-011-0441-z

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  • DOI: https://doi.org/10.1007/s11253-011-0441-z

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