{"ID":2857577,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.09368","arxiv_id":"2510.09368","title":"Characterizing Maximal Monotone Operators with Unique Representation","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-Nikodým 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.","short_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-...","url_abs":"https://arxiv.org/abs/2510.09368","url_pdf":"https://arxiv.org/pdf/2510.09368v1","authors":"[\"Sotiris Armeniakos\",\"Aris Daniilidis\"]","published":"2025-10-10T13:24:13Z","proceeding":"math.FA","tasks":"[\"math.FA\",\"math.OC\"]","methods":"[]","has_code":false}