Nonlinear Carleman operators on Banach lattices

An operator, not necessarily linear, will be called a Carleman operator if the image of the positive elements in the unit ball are bounded in the univ ersal completion of the range space. For certain Banach lattices, a class o f (not necessarily linear) Carleman operators is characterized in terms of an integral representation and in a more general setting as operators satis fying a pointwise finiteness condition. These operators though not linear a re orthogonally additive and monotone.