Unitary Correlation Sets

Abstract

The unitary correlation sets defined by the first author in conjunction with tensor products of Unc(n) are further studied. We show that Connes’ embedding problem is equivalent to deciding whether or not two smaller versions of the unitary correlation sets are equal. Moreover, we obtain the result that Connes’ embedding problem is equivalent to deciding whether or not two cross norms on Mn⊗ Mn are equal for all n≥ 2.