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Numerical peak points and numerical Šilov boundary for holomorphic functions

Author(s): Sung Guen Kim
Journal: Proc. Amer. Math. Soc. 136 (2008), 4339-4347.
MSC (2000): Primary 46A22; Secondary 46G25
Posted: 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 is the complex space or . 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 ${\mathcal A}_{\infty}(B_{l_1}:l_1).$

References:

1.: M. D. Acosta, Boundaries for spaces of holomorphic functions on Publ. Res. Inst. Math. Sci. 42 (2006), 27-44. MR 2215434 (2007j:46073)
2.: M. D. Acosta and S. G. Kim, Denseness of holomorphic functions attaining their numerical radii, Israel J. Math. 161 (2007), 373-386. MR 2350167
3.: M. D. Acosta and S. G. Kim, Numerical boundaries for some classical Banach spaces, to appear in J. Math. Anal. Appl.
4.: M. D. Acosta and M. L. Lourenco, Shilov boundary for holomorphic functions on some classical Banach spaces, Studia Math. 179 (2007), no. 1, 27-39. MR 2291721
5.: E. Bishop, A minimal boundary for function algebras, Pacific J. Math. 9 (1959), 629-642. MR 0109305 (22:191)
6.: F. F. Bonsall and J. Duncan, Numerical ranges II, London Math. Soc. Lecture Note Ser. 10 (Cambridge Univ. Press, 1973). MR 0442682 (56:1063)
7.: T. W. Gamelin, Uniform Algebra, Chelsea, New York, 1984.
8.: J. Globevnik, Boundaries for polydisc algebras in infinite dimensions, Math. Proc. Cambridge Philos. Soc. 85 (1979), 291-303. MR 516088 (80i:46046)
9.: L. Harris, The numerical range of holomorphic functions in Banach spaces, Amer. J. Math. 93 (1971), 1005-1119. MR 0301505 (46:663)
10.: R. A. Ryan, Dunford-Pettis properties, Bull. Acad. Polon. Sci. Math. 27 (1979), 373-379. MR 557405 (80m:46018)

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Additional Information:

Sung Guen Kim
Affiliation: Department of Mathematics, Kyungpook National University, Daegu 702-701, South Korea
Email: sgk317@knu.ac.kr

DOI: 10.1090/S0002-9939-08-09402-1
PII: S 0002-9939(08)09402-1
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
Posted: 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
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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