ε-enlargements of maximal monotone operators in Banach spaces

Abstract. Given a maximal monotone operator T in a Banach space, we consider an enlargement T ε, in which monotonicity is lost up to ε, in a very similar way to the ε-subdifferential of a convex function. We establish in this general framework some theoretical properties of T ε, like a transportation formula, local Lipschitz continuity, local boundedness, and a Brøndsted & Rockafellar property