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

Details The structure of the $W^{*}$--tensor product over a $W^{*}$--subalgebra and its predual ($σ$--finite case) The structure of the $W^{*}$--tensor product over a $W^{*}$--subalgebra and its predual ($σ$--finite case)

2004-11-09

arxiv.org/abs/math/0411203v1

Mathematics

Operator Algebras

12 pages

Scientific paper

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.

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