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.
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
Hits: 3467
Download times: 1833
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
View Full Text  View/Add Comment  Download reader