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Results tagged with oa.operator-algebras
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user 161092
Algebras of operators on Hilbert space, $C^*-$algebras, von Neumann algebras, non-commutative geometry
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Can a non-separable C$^*$ algebra have separable GNS Hilbert space
Suppose we have a $C^*$ algebra $\mathfrak{U}$ that is non-separable. Consider a state $ω$ of $\mathfrak{U}$ and the GNS representation $(H_ω,π_ω,Ω)$. Is it possible for $H_ω$ to be separable, and if …
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