Countably generated Douglas algebras

Author:
Keiji Izuchi

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

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Abstract: Under a certain assumption of and in which is considered by Sarason, a strong separation theorem is proved. This is available to study a Douglas algebra generated by and . It is proved that (1) ball does not have exposed points for every Douglas algebra , (2) Sarason's three functions problem is solved affirmatively, (3) some characterization of for which is singly generated, and (4) the -ideal conjecture for Douglas algebras is not true.

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DOI:
https://doi.org/10.1090/S0002-9947-1987-0869406-9

Article copyright:
© Copyright 1987
American Mathematical Society