On discretization of C*-algebras
Abstract
The C*-algebra of bounded operators on the separable infinite-dimensional Hilbert space cannot be mapped to a W*-algebra in such a way that each unital commutative C*-subalgebra C(X) factors normally through ∞(X). Consequently, there is no faithful functor discretizing C*-algebras to AW*-algebras, including von Neumann algebras, in this way.
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