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