Cancellability and Regularity of Operator Connections

An operator connection is a binary operation assigned to each pair of positive operators satisfying monotonicity, continuity from above and the transformer inequality. In this paper, we introduce and characterize the concepts of cancellability and regularity of operator connections with respect to operator monotone functions, Borel measures and certain operator equations. In addition, we investigate the existence and the uniqueness of solutions for such operator equations.