Approximation in operator algebras on bounded analytic functions

Author:
M. W. Bartelt

Journal:
Trans. Amer. Math. Soc. **170** (1972), 71-83

MSC:
Primary 46J10

DOI:
https://doi.org/10.1090/S0002-9947-1972-0361791-9

MathSciNet review:
0361791

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Abstract: Let denote the algebra of bounded analytic functions on the open unit disc in the complex plane. Let denote endowed with the strict topology . In 1956, R. C. Buck introduced , the algebra of all continuous linear operators from into . This paper studies the algebra and some of its subalgebras, in the norm topology and in the topology of uniform convergence on bounded subsets. We also study a special class of operators, the translation operators. For an analytic map of the open unit disc into itself, the translation operator is defined on by . In particular we obtain an expression for the norm of the difference of two translation operators.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1972-0361791-9

Keywords:
Bounded analytic functions,
operator algebras,
strict topology,
translation operators

Article copyright:
© Copyright 1972
American Mathematical Society