Matrices of unitary moments

Abstract

We investigate certain matrices composed of mixed, second-order moments of unitaries. The unitaries are taken from C*-algebras with moments taken with respect to traces, or, alternatively, from matrix algebras with the usual trace. These sets are of interest in light of a theorem of E. Kirchberg about Connes' embedding problem.

12 pages. In the revision (to version 2) we add some citations to earlier results on extreme correlation matrices that include some results we use

References in corpus (4)

• Connes' embedding conjecture and sums of hermitian squares
• A simple proof of a theorem of Kirchberg and related results on $C^{\ast }$-norms
• Combinatorial aspects of Connes's embedding conjecture and asymptotic distribution of traces of products of unitaries
• A non-commutative, analytic version of Hilbert's 17-th problem in type II${}_1$ von Neumann algebras

Cited by in corpus (1)

• The Correlation Numerical Range of a Matrix and Connes' Embedding Problem