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arxiv: 1309.3657 · v2 · pith:RXZKCCGZnew · submitted 2013-09-14 · 🧮 math.CV

A counterexample to a theorem of Bremermann on Shilov boundaries

classification 🧮 math.CV
keywords shilovboundariesbremermanncounterexampletheoremwidetildealgebraboundary
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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 $\mathcal A(D)$ coincides with the corresponding one for $\widetilde D$.

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