Functions not vanishing on trivial Gleason parts of Douglas algebras
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- by Pamela Gorkin PDF
- Proc. Amer. Math. Soc. 104 (1988), 1086-1090 Request permission
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 $\left | g \right | \leq \left | f \right |{\text { on }}M(B)$, then $g/f \in B$.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- 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