中文摘要：

在迹极限的意义下，特别是在单代数的条件下，研究某些C^＊-代数性质的封闭性，假设A=（t2）lim n→∞（An,pn）,An上至少有一个迹态或An具有（SP）性质，则A也有相同的结果；假设A=（t3）lim n→∞（An,pn）并且A中单代数，如果TR（An）=0,tsr（An）=1和An具有投影消去律，则A也有相同的结果。

英文摘要：

It was shown that there are some C^＊-algebras maintaining the closing property with the tracial limit, especially under the condition of simplicity. Suppose A = （t2） lim n→∞ （An,pn）. If each An admits at least one tracial state or has SP-property, then A has the same case. Suppose A = （t3）lim n→∞（An,pn） and A is simple. If TR（An） = 0, tsr（An） = 1 and An has Cancelation of Projection, then A has the same case.