Mathematical Research Letters

Volume 20 (2013)

Number 6

The isomorphism relation for separable $C*$-algebras

Pages: 1071 – 1080



George A. Elliott (Department of Mathematics, University of Toronto, Toronto, Ontario, Canada)

Ilijas Farah (Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada)

Vern I. Paulsen (Department of Mathematics, University of Houston, Texas, U.S.A.)

Christian Rosendal (Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, U.S.A.)

Andrew S. Toms (Department of Mathematics, Purdue University, West Lafayette, Indiana, U.S.A.)

Asger Törnquist (Department of Mathematical Sciences, University of Copenhagen, Denmark)


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.

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