Integral Equations and Operator Theory

, Volume 89, Issue 1, pp 125–149 | Cite as

Unitary Correlation Sets

Article

Abstract

The unitary correlation sets defined by the first author in conjunction with tensor products of \(\mathcal {U}_{nc}(n)\) 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 \(M_n \otimes M_n\) are equal for all \(n \ge 2\).

Keywords

Connes’ embedding problem Tsirelson’s problem Unitary correlation sets Cross-norms Operator system tensor products 

Mathematics Subject Classification

Primary 47L25 Secondary 46L99 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of WaterlooWaterlooCanada

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