| Property ∏σ and tensor products of operator algebras |
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| 作者单位： | Jian-hua ZHANG（College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, China） ;
Hong-ke DU（College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, China） ;
Hui-xin CAO（College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, China） ; |
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| 基金项目： | This work was partially supported by the National Natural Science Foundation of China (Grant No. 10571114)and the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No.2004A17) |
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| 摘 要： | In this paper, we introduce Property ∏σ of operator algebras and prove that nest subalgebras and the finite-width CSL subalgebras of arbitrary von Neumann algebras have Property ∏σ.Finally, we show that the tensor product formula alg ML1-(×)algNL2 = algM-(×)N(L1 (×) L2) holds for any two finite-width CSLs L1 and L2 in arbitrary von Neumann algebras M and N, respectively.
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| 关 键 词： | Property ∏σ tensor product nest subalgebra CSL subalgebra |
| 收稿时间： | 20 April 2007 |
| 修稿时间： | 14 May 2007 |
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