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.
In this paper,we introduce PropertyΠ_σof operator algebras and prove that nest sub- algebras and the finite-width CSL subalgebras of arbitrary von Neumann algebras have PropertyΠ_σ. Finally,we show that the tensor product formula alg_ML_1(?)alg_NL_2=alg_(M(?)N)(L_1(?)L_2) holds for any two finite-width CSLs L_1 and L_2 in arbitrary von Neumann algebras M and N,respectively.
基金
This work was partially supported by the National Natural Science Foundation of China (Grant No.10571114)
the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No.2004A17)
