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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Functions not vanishing on trivial Gleason parts of Douglas algebras


Author: Pamela Gorkin
Journal: Proc. Amer. Math. Soc. 104 (1988), 1086-1090
MSC: Primary 46J10
DOI: https://doi.org/10.1090/S0002-9939-1988-0969050-5
MathSciNet review: 969050
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Abstract: Let $ B$ denote a closed subalgebra of $ {L^\infty }$ containing the space of bounded analytic functions. Let $ M(B)$ denote the maximal ideal space of $ B$. Let $ f$ be a function in $ B$ such that $ f$ does not vanish on any Gleason part consisting of a single point. We show that if $ g$ is a function in $ B$ such that $ \left\vert g \right\vert \leq \left\vert f \right\vert{\text{ on }}M(B)$, then $ g/f \in B$.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0969050-5
Article copyright: © Copyright 1988 American Mathematical Society