## Illinois Journal of Mathematics

### A characterization of $C(K)$ among function algebras on a Riemann surface

Lynette J. Boos

#### Abstract

For a compact subset $K$ of a Riemann surface, necessary and sufficient conditions are given for a function algebra containing $A(K)$ to be all of $C(K)$. Using these results, several conditions are given on a complex-valued function $f$ so that the algebra generated by $A(K)$ and $f$ is all of $C(K)$. In particular, the results are applied to a harmonic function $f$ to give sufficient conditions for the algebra generated by $A(K)$ and $f$ to be all of $C(K)$. Also, sufficient conditions are given for the algebra $A(K)$ to be a maximal subalgebra of $C(K)$.

#### Article information

Source
Illinois J. Math., Volume 52, Number 3 (2008), 867-885.

Dates
First available in Project Euclid: 1 October 2009

https://projecteuclid.org/euclid.ijm/1254403719

Digital Object Identifier
doi:10.1215/ijm/1254403719

Mathematical Reviews number (MathSciNet)
MR2546012

Zentralblatt MATH identifier
1192.46048

#### Citation

Boos, Lynette J. A characterization of $C(K)$ among function algebras on a Riemann surface. Illinois J. Math. 52 (2008), no. 3, 867--885. doi:10.1215/ijm/1254403719. https://projecteuclid.org/euclid.ijm/1254403719

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