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Proceedings of the American Mathematical Society

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Polynomial approximation on three-dimensional real-analytic submanifolds of $\mathbf{C}^n$


Authors: John T. Anderson, Alexander J. Izzo and John Wermer
Journal: Proc. Amer. Math. Soc. 129 (2001), 2395-2402
MSC (2000): Primary 32E30; Secondary 46J10
DOI: https://doi.org/10.1090/S0002-9939-01-05911-1
Published electronically: January 18, 2001
MathSciNet review: 1823924
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Abstract:

It was once conjectured that if $A$ is a uniform algebra on its maximal ideal space $X$ and if each point of $X$ is a peak point for $A$, then $A = C(X)$. This peak point conjecture was disproved by Brian Cole in 1968. However, it was recently shown by Anderson and Izzo that the peak point conjecture does hold for uniform algebras generated by smooth functions on smooth two-manifolds with boundary. Although the corresponding assertion for smooth three-manifolds is false, we establish a peak point theorem for real-analytic three-manifolds with boundary.


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Additional Information

John T. Anderson
Affiliation: Department of Mathematics, College of the Holy Cross, Worcester, Massachusetts 01610
Email: anderson@math.holycross.edu

Alexander J. Izzo
Affiliation: Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403
Address at time of publication: Department of Mathematics, Texas A & M University, College Station, Texas 77843
Email: aizzo@math.bgsu.edu, aizzo@math.tamu.edu

John Wermer
Affiliation: Department of Mathematics, Brown University, Providence, Rhode Island 02912
Email: wermer@math.brown.edu

DOI: https://doi.org/10.1090/S0002-9939-01-05911-1
Received by editor(s): December 28, 1999
Published electronically: January 18, 2001
Communicated by: Steven R. Bell
Article copyright: © Copyright 2001 American Mathematical Society