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A PEAK POINT THEOREM FOR UNIFORM ALGEBRAS GENERATED BY SMOOTH FUNCTIONS ON TWO-MANIFOLDS

Published online by Cambridge University Press:  09 April 2001

JOHN T. ANDERSON  and
ALEXANDER J. IZZO
JOHN T. ANDERSON
Affiliation:
Department of Mathematics, College of the Holy Cross, Worcester, MA 01610, USA; e-mail: anderson@math.holycross.edu
ALEXANDER J. IZZO
Affiliation:
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA Current address: Department of Mathematics, Texas A & M University, College Station, TX 77843, USA; e-mail: aizzo@math.bgsu.edu
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Abstract

We establish the peak point conjecture for uniform algebras generated by smooth functions on two-manifolds: if A is a uniform algebra generated by smooth functions on a compact smooth two-manifold M, such that the maximal ideal space of A is M, and every point of M is a peak point for A, then A = C(M). We also give an alternative proof in the case when the algebra A is the uniform closure P(M) of the polynomials on a polynomially convex smooth two-manifold M lying in a strictly pseudoconvex hypersurface in Cn.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 2 , March 2001 , pp. 187 - 195
Copyright
© The London Mathematical Society 2001

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Footnotes

This paper was presented to the American Mathematical Society in January 1999.