C^*-代数包含的归一化器和近似单位

IF 1.2 2区数学 Q1 MATHEMATICS

Indiana University Mathematics Journal Pub Date : 2023-01-01 DOI:10.1512/iumj.2023.72.9539

David R. Pitts

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引用次数: 1

摘要

对于包含C*-代数$D\subseteq A$和$D$阿贝尔，我们证明了当$n\在A$中归一化$D$时，$n^*n$和$nn^*$与$D$交换。作为推论，当$D$是$ a $中的正则MASA时，$D$的每一个近似单位也是$ a $的近似单位。这允许在非单情况下从Cartan MASA的定义中去除非简并假设。

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Normalizers and approximate units for inclusions of C^*-algebras

For an inclusion of C*-algebras $D\subseteq A$ with $D$ abelian, we show that when $n\in A$ normalizes $D$, $n^*n$ and $nn^*$ commute with $D$. As a corollary, when $D$ is a regular MASA in $A$, every approximate unit for $D$ is also an approximate unit for $A$. This permits removal of the non-degeneracy hypothesis from the definition of a Cartan MASA in the non-unital case.

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