Journal of East China Normal University(Natural Science) >

2016 , Vol. 2016 >Issue 2: 30 - 34

DOI: https://doi.org/2016.02.004

Article

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

  • JIANG Run-Liang
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Received date: 2015-03-31

  Online published: 2016-07-25

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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.

Key words： commutative C^*-algebras; enveloping Von Neumannalgebra

Cite this article

JIANG Run-Liang . A note on the commutativity of {C}^*-algebras[J]. Journal of East China Normal University(Natural Science), 2016 , 2016(2) : 30 -34 . DOI: 2016.02.004

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