Mean matrices and infinite divisibility

We consider matrices M with entries mij = m(λi, λj) where λ1, … ,λn are positive numbers and m is a binary mean dominated by the geometric mean, and matrices W with entries wij = 1/m (λi, λj) where m is a binary mean that dominates the geometric mean. We show that these matrices are infinitely divisible for several much-studied classes of means.