A dichotomy for the Mackey Borel structure

Ilijas Farah

A dichotomy for the Mackey Borel structure

Operator Algebras 2010-02-01 v2 Logic

Authors: Ilijas Farah

Abstract

We prove that the equivalence of pure states of a separable C*-algebra is either smooth or it continuously reduces $[0,1]^{\bbN}/\ell_2$ and it therefore cannot be classified by countable structures. The latter was independently proved by Kerr--Li--Pichot by using different methods. We also give some remarks on a 1967 problem of Dixmier.

Keywords

c*-algebras

Cite

@article{arxiv.0908.1943,
  title  = {A dichotomy for the Mackey Borel structure},
  author = {Ilijas Farah},
  journal= {arXiv preprint arXiv:0908.1943},
  year   = {2010}
}

Comments

To appear in Proceedings of the Asian Logic Colloquium

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