Tracial Limit of C~*-algebras

摘要

A new limit of C~*-algebras, the tracial limit, is introduced in this paper. We show that a separable simple C~*-algebra A is a tracial limit of C~*-algebras in I~((k)) if and only if A has tracial topological rank no more than k. We present several known results using the notion of tracial limits.