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Numerical peak points and numerical Šilov boundary for holomorphic functions

Author: Sung Guen Kim
Journal: Proc. Amer. Math. Soc. 136 (2008), 4339-4347
MSC (2000): Primary 46A22; Secondary 46G25
Published electronically: June 3, 2008
MathSciNet review: 2431048
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Abstract: In this paper, we characterize the numerical and numerical strong-peak points for $ {\mathcal A}_{\infty}(B_{E}:E)$ when $ E$ is the complex space $ l_1$ or $ C(K)$. We also prove that $ \{(x, x^*)\in \Pi(l_1):\vert x^*(e_n)\vert=1~$for all$ ~n\in \mathbb{N} \}$ is the numerical Šilov boundary for $ {\mathcal A}_{\infty}(B_{l_1}:l_1).$

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Sung Guen Kim
Affiliation: Department of Mathematics, Kyungpook National University, Daegu 702-701, South Korea

Keywords: Numerical peak points, numerical Silov boundaries
Received by editor(s): September 9, 2006
Received by editor(s) in revised form: July 16, 2007, October 18, 2007, and October 23, 2007
Published electronically: June 3, 2008
Additional Notes: The author thanks the referee for invaluable suggestions and for help with an earlier version of this paper.
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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