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Localization for uniform algebras generated by real-analytic functions


Authors: John T. Anderson and Alexander J. Izzo
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 46J10, 46J15; Secondary 32A38, 32A65
DOI: https://doi.org/10.1090/proc/13640
Published electronically: June 22, 2017
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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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Additional Information

John T. Anderson
Affiliation: Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, Massachusetts 01610
Email: janderso@holycross.edu

Alexander J. Izzo
Affiliation: Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403
Email: aizzo@bgsu.edu

DOI: https://doi.org/10.1090/proc/13640
Received by editor(s): May 30, 2016
Received by editor(s) in revised form: December 24, 2016
Published electronically: June 22, 2017
Communicated by: Franc Forstneric
Article copyright: © Copyright 2017 American Mathematical Society