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 ${\ell }^{\infty }(X)$. Consequently, there is no faithful functor discretizing C*-algebras to AW*-algebras, including von Neumann algebras, in this way.

5 pages. Please note that arXiv:1607.03376 supersedes this paper. It significantly strengthens the main results and includes positive results on discretization of C*-algebras