Abstract
We construct an example of a maximal unimodular Dirichlet algebra whose one-point Gleason parts are dense in the maximal ideal space. The main statements were announced in [1] and now we provide their complete proofs.
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References
Yashagin E. I., “On one-point Gleason parts of Blaschke algebras,” Funktsional. Anal., 40, No. 1, 92–94 (2006).
Wermer J., “Dirichlet algebras,” J. Duke Math., 27, No. 3, 373–382 (1960).
Gamelin T. W., Uniform Algebras [Russian translation], Mir, Moscow (1973).
Browder A., Introduction to Function Algebras, Benjamin, New York (1969).
Basener W. G., “On ratioconvex hulls,” Trans. Amer. Math. Soc., 182, No. 455, 353–381 (1973).
Grigoryan S. A. and Tonev T. V., “Blaschke inductive limit of uniform algebras,” Internat. J. Math. Math. Sci., 27, No. 10, 599–620 (2001).
Forster O. F., Riemann Surfaces [Russian translation], Mir, Moscow (1980).
Garnett J., Bounded Analytic Functions [Russian translation], Mir, Moscow (1984).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 4, pp. 949–954, July–August, 2007.
Original Russian Text Copyright © 2007 Yashagin E. I.
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Yashagin, E.I. An example of a maximal unimodular Dirichlet algebra. Sib Math J 48, 762–766 (2007). https://doi.org/10.1007/s11202-007-0077-2
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DOI: https://doi.org/10.1007/s11202-007-0077-2