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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
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
Citation:
V. M. Gichev, “Invariant Function Algebras on Compact Commutative Homogeneous Spaces”, Mosc. Math. J., 8:4 (2008), 697–709
Linking options:
https://www.mathnet.ru/eng/mmj326 https://www.mathnet.ru/eng/mmj/v8/i4/p697
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