Characterizing Maximal Monotone Operators with Unique Representation
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917003157045248 |
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| author | Armeniakos, Sotiris Daniilidis, Aris |
| author_facet | Armeniakos, Sotiris Daniilidis, Aris |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09368 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterizing Maximal Monotone Operators with Unique Representation Armeniakos, Sotiris Daniilidis, Aris Functional Analysis Optimization and Control 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. |
| title | Characterizing Maximal Monotone Operators with Unique Representation |
| topic | Functional Analysis Optimization and Control |
| url | https://arxiv.org/abs/2510.09368 |