Strong mixing coefficients for non-commutative Gaussian processes

Bounds for non-commutative versions of two classical strong mixing coefficients for q-Gaussian processes are found in terms of the angle between the underlying Hilbert spaces. As a consequence, we construct a psi-mixing q-Gaussian stationary sequence with growth conditions on variances of partial sums. If classical processes with analogous properties were to exist, they would provide a counter-example to the Ibragimov conjecture.