Characterizing Maximal Monotone Operators with Unique Representation

Abstract

We study maximal monotone operators whose Fitzpatrick family reduces to a singleton; such operators will be called uniquely representable. We show that every such operator is cyclically monotone (hence, for some convex function ) if and only if it is 3-monotone. In Radon-Nikodým spaces, under mild conditions (which become superfluous in finite dimensions), we prove that a subdifferential operator is uniquely representable if and only if is the sum of a support and an indicator function of suitable convex sets.