Subalgebras generated by extreme points in Fourier–Stieltjes algebras of locally compact groups
Volume 202 / 2011
Studia Mathematica 202 (2011), 289-302
MSC: Primary 43A30, 43A35, 43A40; Secondary 46J10.
DOI: 10.4064/sm202-3-5
Abstract
Let $G$ be a locally compact group, $G^*$ be the set of all extreme points of the set of normalized continuous positive definite functions of $G$, and $a(G)$ be the closed subalgebra generated by $G^*$ in $B(G)$. When $G$ is abelian, $G^*$ is the set of Dirac measures of the dual group $\hat{G}$, and $a(G)$ can be identified as $l^1(\hat{G})$. We study the properties of $a(G)$, particularly its spectrum and its dual von Neumann algebra.
