Properties of strongly infinite C*-algebras
Properties of strongly infinite C*-algebras
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强无穷 C* 代数的性质
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Liang, Yue-liang
中科院分区：
文献类型：
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作者：
Liang, Yue-liang
给出了C*-代数迹极限的等价形式，并从正元的比较引入了强无限C*-代数的定义，在研究强无限C*-代数与纯无限C*-代数关系的基础上，得到了具有SP-性质的强无限C*-代数的迹极限是强无限的结论，对于给定的秩为真实的的C*-代数A，若A的闭双边理想J和商A/T是强无限的，则A是强无限的，具有SP-性质的强无限C*-代数的非零闭双边理想是强无限的，强无限C*-代数的n个和项的直和是强无限的.
Equivalent form of tracial limit of C*-algebras was obtained,and the definition of strongly infinite C*-algebras is also introduced from the comparison of the positive elements.On the basis of the study of the relationship between the strongly infinite C*-algebras and the purely infinite C*-algebras,it comes to the conclusion that the tracial limit of the strongly infinite C*-algebras with SP-property is strongly infinite.For a given C*-algebra A with real rank zero,if its closed two-sided ideal J and the quotient A/T are strongly infinite,then A is strongly infinite.Non-zero closed two-sided ideals of the strongly infinite C*-algebras with SP-property are strongly infinite.Direct sum of n summands of a strongly infinite C*-algebra is strongly infinite.