Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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?)

  • [1] S. Banach, Théorie des opérations linéaires, Chelsea, New York, 1955.
  • [2] John B. Conway, Subnormal operators, Research Notes in Mathematics, vol. 51, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1981. MR 634507
  • [3] Raúl E. Curto and Norberto Salinas, Generalized Bergman kernels and the Cowen-Douglas theory, Amer. J. Math. 106 (1984), no. 2, 447–488. MR 737780, 10.2307/2374310
  • [4] J. Dixmier, Les algèbres d'opérateur dans l'espace hilbertien, Gauthier-Villars, Paris, 1957.
  • [5] D. Sarason, Weak-star density of polynomials, J. Reine Angew. Math. 252 (1972), 1-15.
  • [6] -, Weak-star generators of $ {H^\infty }$, Pacific J. Math. 17 (1966), 519-528.

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Keywords: Spectral set, weak-star closed algebra, generalized Bergman kernel
Article copyright: © Copyright 1984 American Mathematical Society