The Sum Theorem for Linear Maximal Monotone Operators
M.D. Voisei
TL;DR
This paper proves that the sum of two linear maximal monotone operators is also maximal, confirming a longstanding conjecture in the field of monotone operator theory.
Contribution
It provides a positive proof of Rockafellar's sum conjecture specifically for linear maximal monotone operators, advancing theoretical understanding.
Findings
Confirmed maximality of the sum of linear maximal monotone operators
Extended the class of operators for which the sum theorem holds
Resolved a longstanding open problem in monotone operator theory
Abstract
The goal of this article is to give a positive answer to Rockafellar's maximality of the sum conjecture in the linear multi-valued operator case.
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Taxonomy
TopicsDifferential Equations and Boundary Problems · Numerical methods in inverse problems · Contact Mechanics and Variational Inequalities