Localization for uniform algebras generated by real-analytic functions

Anderson, John; Izzo, Alexander

doi:10.1090/proc/13640

Localization for uniform algebras generated by real-analytic functions
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by John T. Anderson and Alexander J. Izzo PDF

Proc. Amer. Math. Soc. 145 (2017), 4919-4930 Request permission

Abstract:

It is shown that if $A$ is a uniform algebra generated by real-analytic functions on a suitable compact subset $K$ of a real-analytic variety such that the maximal ideal space of $A$ is $K$ and every continuous function on $K$ is locally a uniform limit of functions in $A$, then $A=C(K)$. This gives an affirmative answer to a special case of a question from the Proceedings of the Symposium on Function Algebras held at Tulane University in 1965.

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