The classification problem for finitely generated operator systems and spaces [article]

Martín Argerami, Samuel Coskey, Mehrdad Kalantar, Matthew Kennedy, Martino Lupini, Marcin Sabok
2015 arXiv   pre-print
The classification of separable operator spaces and systems is commonly believed to be intractable. We analyze this belief from the point of view of Borel complexity theory. On one hand we confirm that the classification problems for arbitrary separable operator systems and spaces are intractable. On the other hand we show that the finitely generated operator systems and spaces are completely classifiable (or smooth); in fact a finitely generated operator system is classified by its complete
more » ... ory when regarded as a structure in continuous logic. In the particular case of operator systems generated by a single unitary, a complete invariant is given by the spectrum of the unitary up to a rigid motion of the circle, provided that the spectrum contains at least 5 points. As a consequence of these results we show that the relation on compact subsets of C^n, given by homeomorphism via a degree 1 polynomial, is smooth.
arXiv:1411.0512v3 fatcat:vzw556d7fncu5oggvko7lctubm