| PrO-C*-代数的顺从性和核性 |
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| 引用本文： | 许天周,李炳照,赵雨耿.PrO-C*-代数的顺从性和核性[J].数学进展,2003,32(3):334-340. |
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| 作者姓名： | 许天周 李炳照 赵雨耿 |
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| 作者单位： | 北京理工大学应用数学系,北京,100081,中国 |
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| 摘 要： | 研究了Pro—C^*-代数的顺从性和核性．主要证明了(1)顺从Pro—C^*代数的闭理想是顺从的；(2)核Pro—C^*代数类对归纳极限封闭；(3)交换σ-C^*-代数和核C^*-代数都是核，σ-C^*-代数并且核σ-C^*-代数类对于商运算、张量积运算和可数逆向极限封闭．进一步得到核，σ-C^*-代数的扩张保持核性的条件。
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| 关 键 词： | Pro－C^＊－代数 顺从性 核性 闭理想 归纳极限 封闭性 σ－C^＊－代数 Banach代数 lmc－C^＊－代数 |
Amenability and Nuclearity for Pro-C*-Algebras |
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| XU Tian-zhou,LI Bing-zhao,ZHAO Yu-geng.Amenability and Nuclearity for Pro-C*-Algebras[J].Advances in Mathematics,2003,32(3):334-340. |
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| Authors: | XU Tian-zhou LI Bing-zhao ZHAO Yu-geng |
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| Abstract: | Any closed ideal of an amenable Pro-C*-algebra (inverse limit of C*-algebras)is amenable. The class of nuclear Pro-C*-algebras is closed under inductive limits. In par-ticular, the class of nuclear σ-C*-algebras contains all commutative σ-C*-algebras and allnuclear C*-algebras, and is closed under quotients, tensor products and countable inverselimits. Extensions of nuclear σ-C*algebras by nuclear σ-C*-algebras are themselves nuclear. |
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| Keywords: | Pro-C*-algebra amenability nuclearity exact sequence |
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