The ideal separation property for reduced group $C^*$-algebras

Are Austad, Hannes Thiel
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Abstract

We say that an inclusion of a $*$-algebra $A$ into a $C^*$-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 $L^1(G) \subseteq C^*_{\mathrm{red}}(G)$ has the ideal separation property.
还原组 $C^*$ 算法的理想分离特性
如果 $B$ 中的封闭理想可以通过它们与 $A$ 的交集恢复,我们就说 $*$-algebra $A$ 对 $C^*$-algebra $B$ 的包含具有理想分离性质。从谐波分析和非交换几何的角度来看,这种夹杂具有诱人的性质。我们建立了局部紧凑群的多个永久性质,其中 $L^1(G)\subseteq C^*_{\mathrm{red}}(G)$ 具有理想分离性质。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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