The structure of the $W^{\ast }$--tensor product over a $W^{\ast }$--subalgebra and its predual ($\sigma$--finite case)

Abstract

Let $M$, $N$, $R$ be $W^{\ast }$--algebras, with $R$ unitally embedded in both $M$ and $N$. by using Reduction Theory, we extend the previous description of the $W^{\ast }$--tensor product $M{\bar{\otimes }}_{R}N$ over the common $W^{\ast }$--subalgebra $R$ and its predual $(M{\bar{\otimes }}_{R}N{)}_{\ast }$ to the $\sigma$--finite case.

12 pages