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# Mathematical Research Letters

## Volume 20 (2013)

### Number 6

### The isomorphism relation for separable $C*$-algebras

Pages: 1071 – 1080

DOI: http://dx.doi.org/10.4310/MRL.2013.v20.n6.a6

#### Authors

#### Abstract

We prove that the isomorphism relation for separable $C*$-algebras, the relations of complete and $n$-isometry for operator spaces, and the relations of unital $n$-order isomorphisms of operator systems, are Borel reducible to the orbit equivalence relation of a Polish group action on a standard Borel space.