C^*-代数交换性简谈(英)

交换; 代数有许多特征; 在本文中; 证明了; 代数; 是非交换的当且仅当其包络冯诺依曼代数; 中有一个; 子代数; 同构于; 阶矩阵代数; 基于这个性质; 又可以得到一些旧命题的新证明方法

doi:2016.02.004

文章导航 > 华东师范大学学报（自然科学版） > 2016 > (2): 30-34

交换, 代数有许多特征, 在本文中, 证明了, 代数, 是非交换的当且仅当其包络冯诺依曼代数, 中有一个, 子代数, 同构于, 阶矩阵代数, 基于这个性质, 又可以得到一些旧命题的新证明方法, . C^*-代数交换性简谈(英)[J]. 华东师范大学学报（自然科学版）, 2016, (2): 30-34. doi: 2016.02.004

引用本文:

There are, many characterizations, for commutative, In this, we prove, that a, A is, not commutative, if and, only if, there is, a C, B in, the enveloping, Von Neumann, algebra of, such that, B is, isomorphic to, mathrm M, In terms, of this, we can, recover some, characterizations for, the commutativity, of C, algebras appeared. A note on the commutativity of {C}^*-algebras[J]. Journal of East China Normal University (Natural Sciences), 2016, (2): 30-34. doi: 2016.02.004

Citation:

There are, many characterizations, for commutative, In this, we prove, that a, A is, not commutative, if and, only if, there is, a C, B in, the enveloping, Von Neumann, algebra of, such that, B is, isomorphic to, mathrm M, In terms, of this, we can, recover some, characterizations for, the commutativity, of C, algebras appeared. A note on the commutativity of {C}^*-algebras[J]. Journal of East China Normal University (Natural Sciences), 2016, (2): 30-34. doi: 2016.02.004

引用本文:

Citation:

There are, many characterizations, for commutative, In this, we prove, that a, A is, not commutative, if and, only if, there is, a C, B in, the enveloping, Von Neumann, algebra of, such that, B is, isomorphic to, mathrm M, In terms, of this, we can, recover some, characterizations for, the commutativity, of C, algebras appeared. A note on the commutativity of {C}^*-algebras[J]. Journal of East China Normal University (Natural Sciences), 2016, (2): 30-34. doi: 2016.02.004

C^*-代数交换性简谈(英)

doi: 2016.02.004

1.
上海师范大学~~数学系, 上海 200234

详细信息

作者简介:
蒋闰良, 男, 博士后, 研究方向为算子代数. E-mail:Eugene_Jiang@126.com

蒋闰良, 男, 博士后, 研究方向为算子代数. E-mail:Eugene_Jiang@126.com

中图分类号: O212.4
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出版历程
- 收稿日期: 2015-03-31
- 刊出日期: 2016-03-25

A note on the commutativity of {C}^*-algebras

摘要

摘要: 交换C^*-代数有许多特征. 在本文中,证明了~C^*-代数~\mathcal{A}~是非交换的当且仅当其包络冯诺依曼代数~\mathcal{A}''~中有一个~C^*-子代数~\mathcal{B},\mathcal{B}-同构于2阶矩阵代数~\mathrm M_2(\C). 基于这个性质,又可以得到一些旧命题的新证明方法
- 交换~C^*-代数 /
- 包络冯诺依曼代数
Abstract: There are many characterizations for commutative C^*-algebras. In this note, we prove that a C^*-algebra $\mathcal{A} is not commutative if and only if there is a C^*-subalgebra \mathcal{B} in \mathcal{A}'' (the enveloping Von Neumann algebra of mathcal{A}) such that mathcal{B} is-isomorphic to mathrm M_2(\mathcal{\textbf{C}}). In terms of this result, we can recover some characterizations for the commutativity of C^-algebras appeared before.
- commutative C^*-algebras enveloping Von Neumannalgebra /

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参考文献(1)

[1]

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[6] JI G X, TOMIYAMA J. On characterizations of commutativity of C^-algebras [J]. Proceedings of the American Mathematical Society, 2003, 131: 3845-3849.
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[8] MURPHY J G. C^-Algebras and Operator Theory [M]. San Diego: Academic Press, 1990.

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