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Moscow Mathematical Journal, 2008, Volume 8, Number 4, Pages 697–709
DOI: https://doi.org/10.17323/1609-4514-2008-8-4-697-709
(Mi mmj326)
 

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

Invariant Function Algebras on Compact Commutative Homogeneous Spaces

V. M. Gichev

Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science
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Abstract: Let $M$ be a commutative homogeneous space of a compact Lie group $G$ and $A$ be a closed $G$-invariant subalgebra of the Banach algebra $C(M)$. A function algebra is called antisymmetric if it does not contain nonconstant real functions. By the main result of this paper, $A$ is antisymmetric if and only if the invariant probability measure on $M$ is multiplicative on $A$. This implies, for example, the following theorem: if $G^\mathbb C$ acts transitively on a Stein manifold $\mathcal M$, $v\in\mathcal M$, and the compact orbit $M=Gv$ is a commutative homogeneous space, then $M$ is a real form of $\mathcal M$.
Key words and phrases: invariant function algebra, commutative homogeneous space, maximal ideal space.
Received: December 4, 2007
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Language: English
Citation: V. M. Gichev, “Invariant Function Algebras on Compact Commutative Homogeneous Spaces”, Mosc. Math. J., 8:4 (2008), 697–709
Citation in format AMSBIB
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\by V.~M.~Gichev
\paper Invariant Function Algebras on Compact Commutative Homogeneous Spaces
\jour Mosc. Math.~J.
\yr 2008
\vol 8
\issue 4
\pages 697--709
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\crossref{https://doi.org/10.17323/1609-4514-2008-8-4-697-709}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2499352}
\zmath{https://zbmath.org/?q=an:1170.46044}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000261829900005}
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