2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168330As in the cases of freeness and monotonic independence, the notion of conditional freeness is meaningful when complex-valued states are replaced by positive conditional expectations. In this framework, the paper presents several positivity results, a version of the central limit theorem and an analogue of the conditionally free R-transform constructed by means of multilinear function series.Final version, publishedOperator AlgebrasFunctional Analysis46L53; 46L08text