C^*-代数包含的归一化器和近似单位

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research 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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.