拟对角扩张C~*-代数的性质

Some Properties of the Quasidiagonal Extension C~*-algebras

0→J→A→B→0是一个拟对角扩张.证明以下结论:(1)如果J和B具有弱可比性质,则A也具有弱可比性质;(2)如果J和B具有强消去性质,则A也具有强消去性质;(3)如果J和B具有n-无孔性质,则A也具有n-无孔性质.

Let 0→J→A→B→0 be a quasidiagonal extension.We show the following results：（1）suppose that J and B have the weakly comparison properties,then A has the weakly comparison property.（2）suppose that J and Bhave the strictly cancellation properties,then A has the strictly cancellation property.（3） suppose that J and B have the n-unperforated properties,then A has the n-unperforated property.