Property Πσ and tensor products of operator algebras

Abstract

In this paper, we introduce Property Πσ of operator algebras and prove that nest sub- algebras and the finite-width CSL subalgebras of arbitrary von Neumann algebras have Property Πσ. Finally, we show that the tensor product formula algML1⊗algN L2 =a lg M⊗N (L1 ⊗L 2 )h olds for any two finite-width CSLs L1 and L2 in arbitrary von Neumann algebras M and N , respectively.