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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48 .

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Countably generated Douglas algebras
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by Keiji Izuchi PDF
Trans. Amer. Math. Soc. 299 (1987), 171-192 Request permission

Abstract:

Under a certain assumption of $f$ and $g$ in ${L^\infty }$ which is considered by Sarason, a strong separation theorem is proved. This is available to study a Douglas algebra $[{H^\infty }, f]$ generated by ${H^\infty }$ and $f$. It is proved that (1) ball$(B/{H^\infty } + C)$ does not have exposed points for every Douglas algebra $B$, (2) Sarason’s three functions problem is solved affirmatively, (3) some characterization of $f$ for which $[{H^\infty }, f]$ is singly generated, and (4) the $M$-ideal conjecture for Douglas algebras is not true.
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 299 (1987), 171-192
  • MSC: Primary 46J15; Secondary 30D55, 30H05
  • DOI: https://doi.org/10.1090/S0002-9947-1987-0869406-9
  • MathSciNet review: 869406