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Proceedings of the American Mathematical Society

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Douglas algebras which admit codimension 1 linear isometries


Author: Keiji Izuchi
Journal: Proc. Amer. Math. Soc. 129 (2001), 2069-2074
MSC (2000): Primary 46J15, 47B38
Published electronically: November 30, 2000
MathSciNet review: 1825919
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Abstract:

Let $B$ be a Douglas algebra and let $B_b$ be its Bourgain algebra. It is proved that $B$ admits a codimension 1 linear isometry if and only if $B \not= B_b$. This answers the conjecture of Araujo and Font.


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Additional Information

Keiji Izuchi
Affiliation: Department of Mathematics, Niigata University, Niigata 950-2181, Japan
Email: izuchi@math.sc.niigata-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-00-05842-1
Received by editor(s): November 15, 1999
Published electronically: November 30, 2000
Additional Notes: Supported by Grant-in-Aid for Scientific Research (No.10440039), Ministry of Education, Science and Culture.
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2000 American Mathematical Society