2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/218777We prove that the functions t -> (t^q-1)(t^p-1)^{-1} are operator monotone in the positive half-axis for 0 < p < q < 1, and we calculate the two associated canonical representation formulae. The result is used to find new monotone metrics (quantum Fisher information) on the state space of quantum systems.An author has quit and some material addedOperator AlgebrasMathematical Physicstext