C*-代数交换性简谈（英文）

A note on the commutativity of C*-algebras

交换C*-代数有许多特征。在本文中,证明了C*-代数A是非交换的当且仅当其包络冯诺依曼代数A"中有一个C*-子代数B,B*-同构于2阶矩阵代数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.

There are many characterizations for commutative C^＊-algebras. In this note, we prove that a C^＊-algebra .4 is not commutative if and only if there is a C^＊-subalgebra B in A″ （the enveloping Von Neumann algebra of .4） such that B is ＊-isomorphic to M2（C）. In terms of this result, we can recover some characterizations for the commutativity of C^＊- algebras appeared before.