# Tagged Questions

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### Kadison-Singer problem in exotic Hilbert spaces

The Kadison-Singer problem is considered in relation to the separable Hilbert space:
KS: Does every pure state on the diagonal (atomic) masa of $B(\ell_2)$ has a unique extension to $B(\ell_2)$?
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### Do separable $C^*$-algebras form a set?

The question is in subject.
Update: See Andreas Thom's answer.