A dichotomy for the Mackey Borel structure
classification
🧮 math.OA
math.LO
keywords
algebraborelcannotclassifiedcontinuouslycountabledichotomydifferent
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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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