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New counterexamples challenge Rockafellar's sum conjecture in operator theory

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This paper presents counterexamples to Rockafellar's sum conjecture regarding maximally monotone operators. The authors construct specific cases on the sequence spaces $c_0$ and $\ell^1$ where the sum of two maximally monotone operators, despite satisfying the interior-domain condition, is not maximally monotone. A general construction theorem is introduced to compute the monotone polar of certain graphs and establish conditions for maximal monotonicity, which is then applied to derive the counterexamples. AI

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New counterexamples challenge Rockafellar's sum conjecture in operator theory

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  1. Hugging Face Daily Papers TIER_1 English(EN) ·

    Nonmaximal sums of maximally monotone operators under Rockafellar's constraint qualification

    We construct counterexamples to Rockafellar's sum conjecture in which two maximally monotone operators satisfy the interior-domain condition but their sum is not maximally monotone. We give one counterexample on $c_0$ and another on $\ell^1$ with its usual norm. We establish a ge…

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