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Strongly exposed points in uniform algebras

Author(s): Paul Beneker; Jan Wiegerinck
Journal: Proc. Amer. Math. Soc. 127 (1999), 1567-1570.
MSC (1991): Primary 46E99; Secondary 46J10
Posted: February 4, 1999
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Abstract: In this paper we show that the unit ball of an infinite dimensional function algebra has no strongly exposed points.

References:

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R.R. Phelps, Extreme points in function algebras, Duke Math. J. 32 (1965), 267-277. MR 31:3890

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S. Fisher, Exposed points in spaces of bounded analytic functions, Duke Math. J. 36 (1969), 479-484. MR 41:4247

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E. Amar and A. Lederer, Points exposés de la boule unité de $H^\infty(D)$, C.R. Acad. Sci. Paris Sér. A-B 272 (1971), A449-A452. MR 44:788

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G.M. Leibowitz, Lectures on Complex Functions, Scott, Foresman and Company (1970). MR 55:1072

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E.L. Stout, The theory of uniform algebras, Bogden & Quigley (1971). MR 54:11066

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R.R. Phelps, Dentability and extreme points in Banach spaces, J. Funct. Anal. 17 (1974), 78-90. MR 50:5427

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Additional Information:

Paul Beneker
Affiliation: Faculty of Mathematics, Computer Science, Physics and Astronomy (WINS), University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands
Email: beneker@wins.uva.nl

Jan Wiegerinck
Affiliation: Faculty of Mathematics, Computer Science, Physics and Astronomy (WINS), University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands
Email: janwieg@wins.uva.nl

DOI: 10.1090/S0002-9939-99-05274-0
PII: S 0002-9939(99)05274-0
Keywords: Strongly exposed point, function algebra
Received by editor(s): April 20, 1998
Received by editor(s) in revised form: October 6, 1998
Posted: February 4, 1999
Additional Notes: The research of the first author was supported by the Netherlands research organization NWO
Communicated by: Dale Alspach
Copyright of article: Copyright 1999, American Mathematical Society

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