The ideal separation property for reduced group $C^{\ast }$-algebras

Abstract

We say that an inclusion of an algebra $A$ into a $C^{\ast }$-algebra $B$ has the ideal separation property if closed ideals in $B$ can be recovered by their intersection with $A$. Such inclusions have attractive properties from the point of view of harmonic analysis and noncommutative geometry. We establish several permanence properties of locally compact groups for which $L^1(G)\subseteq C_{\mathrm{red}}^{\ast }(G)$ has the ideal separation property.

arXiv commentJ. Funct. Anal. (JFA), to appear. Minor changes, accepted version, 24 pages