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arXiv · 2510.09368

Characterizing Maximal Monotone Operators with Unique Representation

Sotiris Armeniakos·Aris Daniilidis
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Abstract

We study maximal monotone operators $A : X \rightrightarrows X^*$ whose Fitzpatrick family reduces to a singleton; such operators will be called uniquely representable. We show that every such operator is cyclically monotone (hence, $A=\partial f$ for some convex function $f$) if and only if it is 3-monotone. In Radon-Nikod\'{y}m spaces, under mild conditions (which become superfluous in finite dimensions), we prove that a subdifferential operator $A=\partial f$ is uniquely representable if and only if $f$ is the sum of a support and an indicator function of suitable convex sets.

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Sotiris Armeniakos, Aris Daniilidis. 2025-10-10. Characterizing Maximal Monotone Operators with Unique Representation. https://arxiv.org/abs/2510.09368

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