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A counterexample to a theorem of Bremermann on Shilov boundaries


Authors: Marek Jarnicki and Peter Pflug
Journal: Proc. Amer. Math. Soc. 143 (2015), 1675-1677
MSC (2010): Primary 32D10, 32D15, 32D25
DOI: https://doi.org/10.1090/S0002-9939-2014-12384-7
Published electronically: December 11, 2014
MathSciNet review: 3314080
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Abstract | References | Similar Articles | Additional Information

Abstract: We give a counterexample to the following theorem of Bremermann on Shilov boundaries: if $ D$ is a bounded domain in $ \mathbb{C}^n$ having a univalent envelope of holomorphy, say $ \widetilde {D}$, then the Shilov boundary of $ D$ with respect to the algebra $ \mathcal {A}(D)$, call it $ \partial _SD$, coincides with the corresponding one for $ \widetilde {D}$, called $ \partial _S\widetilde {D}$.


References [Enhancements On Off] (What's this?)

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Additional Information

Marek Jarnicki
Affiliation: Jagiellonian University, Faculty of Mathematics and Computer Science, Institute of Mathematics, Łojasiewicza 6, 30-348 Kraków, Poland
Email: Marek.Jarnicki@im.uj.edu.pl

Peter Pflug
Affiliation: Carl von Ossietzky Universität Oldenburg, Institut für Mathematik, Postfach 2503, D-26111 Oldenburg, Germany
Email: Peter.Pflug@uni-oldenburg.de

DOI: https://doi.org/10.1090/S0002-9939-2014-12384-7
Keywords: Shilov boundary, Bergman boundary
Received by editor(s): September 14, 2013
Published electronically: December 11, 2014
Additional Notes: The research was partially supported by grant no. UMO-2011/03/B/ST1/04758 of the Polish National Science Center (NCN)
Communicated by: Franc Forstneric
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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