| A Note on the Monotone Product of Nuclear $C^{*}$-Algebras |
| Received:April 02, 2007 Revised:November 22, 2007 |
| Key Words:
monotone product GNS representations nuclear $C^{*}$-algebras.
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| Fund Project:the Youth Foundation of Sichuan Education Department (No.2003B017); the Doctoral Foundation of Chongqing Normal University (No.08XLB013). |
| Author Name | Affiliation | | WU Wen Ming | College of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, China
Department of Mathematical Science, Tsinghua University, Beijing 100084, China | | ZHAO Yong | School of Mathematics and Information, China-West Normal University, Sichuan 637002, China | | YANG Fang | College of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, China |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2009.03.013 |
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