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Algebras of operators on Hilbert space, $C^*-$algebras, von Neumann algebras, non-commutative geometry

3 votes

If either $A$ is exact or $B$ is nuclear then every closed ideal of $A\otimes_{min}B$ is of ...

When A is simple, it's proved in: https://doi.org/10.1002/mana.201700009 As per the suggestion (below) by leo monsaingeon, here are the details reproduced from above paper: Statement: Let $A$ and $B$ …
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3 votes

Do subgroups have "two sided bases"?

It was recently proved that every regular subfactor (resp., depth 2 subfactor with simple relative commutant) admits a two-sided basis - see http://nyjm.albany.edu/j/2020/26-37.html (resp., https:// …
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0 votes

Results which are known about ideals of spatial tensor product

You can also find some results of that flavor in Closed ideals and Lie ideals of minimal tensor product of certain C*-algebras .
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