On discretization of C*-algebras

Chris Heunen; Manuel L. Reyes

On discretization of C*-algebras

Operator Algebras 2016-08-05 v5 Functional Analysis

Authors: Chris Heunen , Manuel L. Reyes

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.

Keywords

C*-algebras W*-algebras AW*-algebras von Neumann algebras discretization Hilbert space functor

Cite

@article{arxiv.1412.1721,
  title  = {On discretization of C*-algebras},
  author = {Chris Heunen and Manuel L. Reyes},
  journal= {arXiv preprint arXiv:1412.1721},
  year   = {2016}
}

Comments

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

On discretization of C*-algebras

Abstract

Keywords

Cite

Comments

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