On the tensor product of 𝑊* algebras

Renshaw, Bruce B.

doi:10.1090/S0002-9947-1974-0361815-0

On the tensor product of $W^{\ast }$ algebras
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Trans. Amer. Math. Soc. 194 (1974), 337-347 Request permission

Abstract:

We develop the algebra underlying the reduction theory of von Neumann in the language and spirit of Sakai’s abstract ${W^ \ast }$ algebras, and using the maximum spectrum of an abelian von Neumann algebra rather than a measure-theoretic surrogate. We are thus enabled to obtain the basic fact of the von Neumann theory as a special case of a weaker general decomposition theorem, valid without separability or type restrictions, and adapted to comparison with Wright’s theory in the finite case.

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