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Polynomial approximation on three-dimensional real-analytic submanifolds of 
Author(s):
John
T.
Anderson;
Alexander
J.
Izzo;
John
Wermer
Journal:
Proc. Amer. Math. Soc.
129
(2001),
2395-2402.
MSC (2000):
Primary 32E30;
Secondary 46J10
Posted:
January 18, 2001
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Abstract:
It was once conjectured that if  is a uniform algebra on its maximal ideal space  and if each point of  is a peak point for  , then  . 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.
References:
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- H. Alexander and J. Wermer, Several Complex Variables and Banach Algebras, Third edition, Springer, 1998. MR 98g:32002
- 2.
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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:
10.1090/S0002-9939-01-05911-1
PII:
S 0002-9939(01)05911-1
Received by editor(s):
December 28, 1999
Posted:
January 18, 2001
Communicated by:
Steven R. Bell
Copyright of article:
Copyright
2001,
American Mathematical Society
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