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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Approximation in operator algebras on bounded analytic functions
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by M. W. Bartelt PDF
Trans. Amer. Math. Soc. 170 (1972), 71-83 Request permission

Abstract:

Let $B$ denote the algebra of bounded analytic functions on the open unit disc in the complex plane. Let $(B,\beta )$ denote $B$ endowed with the strict topology $\beta$. In 1956, R. C. Buck introduced $[\beta :\beta ]$, the algebra of all continuous linear operators from $(B,\beta )$ into $(B,\beta )$. This paper studies the algebra $[\beta :\beta ]$ 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 $\phi$ an analytic map of the open unit disc into itself, the translation operator ${U_\phi }$ is defined on $B$ by ${U_\phi }f(x) = f(\phi x)$. In particular we obtain an expression for the norm of the difference of two translation operators.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • 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