On the shape of correlation matrices for unitaries
For a positive integer n, we study the collection F_fin (n) formed of all n× n matrices whose entries a_ij, 1≤ i,j≤ n, can be written as a_ij=τ (U_j^*U_i) for some n-tuple U_1, U_2, …, U_n of unitaries in a finite-dimensional von Neumann algebra M with tracial state τ. We show that F_fin (n) is not closed for every n≥ 8. This improves a result by Musat and Rørdam which states the same for n≥ 11. , number=2, journal=MATHEMATICA SCANDINAVICA, author=Mori, Michiya, year=2024, month=May