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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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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Additional Information
  • John T. Anderson
  • Affiliation: Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, Massachusetts 01610
  • MR Author ID: 251416
  • Email: janderso@holycross.edu
  • Alexander J. Izzo
  • Affiliation: Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403
  • MR Author ID: 307587
  • Email: aizzo@bgsu.edu
  • 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
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 4919-4930
  • MSC (2010): Primary 46J10, 46J15; Secondary 32A38, 32A65
  • DOI: https://doi.org/10.1090/proc/13640
  • MathSciNet review: 3692006