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Weak-star closed algebras and generalized Bergman kernels


Author: Karim Seddighi
Journal: Proc. Amer. Math. Soc. 90 (1984), 233-239
MSC: Primary 47B38; Secondary 30C40, 46E20, 46J15, 47A25, 47C05
MathSciNet review: 727240
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Abstract: In this paper we will characterize the weak-star closed algebra $ \mathcal{A}$ generated by the canonical model associated with a generalized Bergman kernel defined on a domain $ G$ in the plane, whose spectrum is a spectral set. In fact, $ \mathcal{A}$ equals the space $ {H^\infty }\left( {{G_0}} \right)$ of all bounded analytic functions on an appropriate set $ {G_0}$ containing $ G$.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0727240-7
Keywords: Spectral set, weak-star closed algebra, generalized Bergman kernel
Article copyright: © Copyright 1984 American Mathematical Society