Divergence operator of regular mappings

Abstract In this paper, we give some generalizations for the filtering of regular operator mappings through a (potentially nonunital) completely positive linear mapping. We find a general formulation of the Jensen operator inequality for convex regular mappings and a unital field of completely positive linear mappings. We introduce the notion of non-commutative F -divergence operators for regular operator mappings and continuous fields of Hilbert space operators and obtain some relations between the perspective of a convex regular mapping and a non-commutative F -divergence operator. We provide a refinement for the general formulation of the Jensen operator inequality and a refinement for the extension of the significant Choi-Davis-Jensen inequality.