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Zapiski Nauchnykh Seminarov LOMI, 1981, Volume 113, Pages 204–207 (Mi znsl3948)  

This article is cited in 1 scientific paper (total in 1 paper)

Short communications

Gleason parts and Choquet boundary of a function algebra on a convex compactum

E. L. Arenson
Full-text PDF (220 kB) Citations (1)
Abstract: Let $K$ be a convex compactum in a complex locally convex space $E$, $P(K)$ be the uniform algebra of functions on $K$ generated by the restrictions of complexaffine continuous functions on $E$. For $x,y\in E$, we set $H(x,y)=\{(1-\lambda)x+\lambda y\colon\lambda\in\mathbb C\}$. It is proved that: (a) the space of maximal ideals of the algebra $P(K)$ coincides with $K$; (b) distinct points $x,y$ from $K$ belong to the same Gleason part if and only if $x$ and $y$ are relatively interior points of the set $H(x,y)\cap K$ (as a subset of $H(x,y)$); (c) the Choquet boundary of the algebra $P(K)$ coincides with the set of complex-extreme points of the compactum $K$ (that is, of points $x$ not belonging to the relative interior of any set of the form $H(x,y)\cap K$ for $y\ne x$).
English version:
Journal of Soviet Mathematics, 1983, Volume 22, Issue 6, Pages 1832–1834
DOI: https://doi.org/10.1007/BF01882582
Bibliographic databases:
Document Type: Article
UDC: 517.54
Language: Russian
Citation: E. L. Arenson, “Gleason parts and Choquet boundary of a function algebra on a convex compactum”, Investigations on linear operators and function theory. Part XI, Zap. Nauchn. Sem. LOMI, 113, "Nauka", Leningrad. Otdel., Leningrad, 1981, 204–207; J. Soviet Math., 22:6 (1983), 1832–1834
Citation in format AMSBIB
\Bibitem{Are81}
\by E.~L.~Arenson
\paper Gleason parts and Choquet boundary of a~function algebra on a~convex compactum
\inbook Investigations on linear operators and function theory. Part~XI
\serial Zap. Nauchn. Sem. LOMI
\yr 1981
\vol 113
\pages 204--207
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl3948}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=629841}
\zmath{https://zbmath.org/?q=an:0515.46047|0472.46039}
\transl
\jour J. Soviet Math.
\yr 1983
\vol 22
\issue 6
\pages 1832--1834
\crossref{https://doi.org/10.1007/BF01882582}
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  • https://www.mathnet.ru/eng/znsl/v113/p204
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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