稳秩1C^＊—代数的几个等价刻画

Some equivalent descriptions on C~*-algebras with stable rank 1

引入酉分解元的概念,给出稳秩1C~*-代数的几个等价刻画,部分回答了D.Handelman的一个问题,并证明了任何稳定有限的单C~*-代数皆可嵌人到具稳秩1的C~*-代数之中。

By introducing the unitary decomposition element, some equivalent descriptions on C~*-algebras with stable rank 1 are presented. And a problem asked by D. Handelman is partially solved. Furthermore, It is proved that every stable finite simple C~*-a]gebras can be embedded into a C~*-algebrawith stable rank 1.