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arXiv · 0908.1943

A dichotomy for the Mackey Borel structure

Ilijas Farah
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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.

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Ilijas Farah. 2010-01-31. A dichotomy for the Mackey Borel structure. https://arxiv.org/abs/0908.1943

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