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强无限~${\bm{C^{\ast}}}$-代数的性质

, PP. 104-114

Keywords: 纯无限~$C,{\ast}$-代数,迹极限,SP-性质

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Abstract:

给出~$C^{\ast}$-代数迹极限的等价形式,从正元的角度提出强无限~$C^{\ast}$-代数的概念.研究了强无限~$C^{\ast}$-代数与纯无限~$C^{\ast}$-代数之间的基本关系,具有SP-性质的强无限~$C^{\ast}$-代数的迹极限为强无限的.对于实秩零的~$C^{\ast}$-代数~$\mathcal{A}$~而言,若闭双边理想~$\mathcal{I}$~及商代数~$\mathcal{A/I}$~为强无限的,则~$\mathcal{A}$~为强无限的.具有SP-性质的强无限~$C^{\ast}$-代数的非零的闭双边理想为强无限的.一个强无限~$C^{\ast}$-代数的有限直和仍然是强无限的.

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