A dichotomy for the Mackey Borel structure

Details A dichotomy for the Mackey Borel structure A dichotomy for the Mackey Borel structure

2009-08-13

arxiv.org/abs/0908.1943v2

Mathematics

Operator Algebras

To appear in Proceedings of the Asian Logic Colloquium

Scientific paper

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.

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