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edited Dec 17, 2021 at 19:00

LSpice

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tensor Tensor product of a von Neumann algebra and $L_\infty $

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asked Dec 17, 2021 at 7:07

user92646

tensor product of a von Neumann algebra and $L_\infty $

Let $R$ be the hyperfinite $II_1$-factor. We know that $R$ is isomorphic to $R\otimes R$. So, $L_\infty(0,1) \otimes R$ is a von Neumann subalgebra of $R$.

I am not sure whether it is sure for any type $II_1$ von Neumann algebra $M$, i.e., is $L_\infty(0,1) \otimes M$ a von Neumann subalgebra of $M$?

oa.operator-algebras von-neumann-algebras