| 吴文明,赵勇,杨芳.关于核型$C^{*}$代数单调积的注记[J].数学研究及应用,2009,29(3):485~490 |
| 关于核型$C^{*}$代数单调积的注记 |
| A Note on the Monotone Product of Nuclear $C^{*}$-Algebras |
| 投稿时间：2007-04-02 修订日期：2007-11-22 |
| DOI：10.3770/j.issn:1000-341X.2009.03.013 |
| 中文关键词: 单调积 GNS表示 核型$C^{*}$代数. |
| 英文关键词:monotone product GNS representations nuclear $C^{*}$-algebras. |
| 基金项目:四川教育厅青年基金(No.2003B017); 重庆师范大学博士基金(No.08XLB013). |
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| 中文摘要: |
| 设$\varphi_{1}$和$\varphi_{2}$是核型$C^{*}$代数$\mathcal{A}_{1}$和$\mathcal{A}_{2}$上的态,我们证明了单调积$C^{*}$代数$\mathcal{A}_{1}\rhd\mathcal{A}_{2}$是核型的.如果态$\varphi_{1}$和$\varphi_{2}$还是忠实的,则单调积$\mathcal{A}_{1}\rhd\mathcal{A}_{2}$是核型$C^{*}$代数当且仅当$C^{*}$代数$\mathcal{A}_{1}$和$\mathcal{A}_{2}$都是核型$C^{*}$代数. |
| 英文摘要: |
| Given two nuclear $C^{*}$-algebras ${\cal A}_{1}$ and ${\cal A}_{2}$ with states $\varphi_{1}$ and $\varphi_{2}$, we show that the monotone product $C^{*}$-algebra ${\cal A}_{1}\rhd{\cal A}_{2}$ is still nuclear. Furthermore, if both the states $\varphi_{1}$ and $\varphi_{2}$ are faithful, then the monotone product ${\cal A}_{1}\rhd{\cal A}_{2}$ is nuclear if and only if the $C^{*}$-algebras ${\cal A}_{1}$ and ${\cal A}_{2}$ both are nuclear. |
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