English(EN) Nonmaximal sums of maximally monotone operators under Rockafellar's constraint qualification

新的反例挑战算子理论中 Rockafellar 的和猜想

作者 PulseAugur 编辑部 · [1 个来源] · 2026-09-09 17:26

本文提出了 Rockafellar 关于最大单调算子和猜想的反例。作者在序列空间 $c_0$ 和 $\ell^1$ 上构造了特定情况，其中两个最大单调算子的和，尽管满足内域条件，但并非最大单调。引入了一个通用的构造定理来计算某些图的单调极值，并建立最大单调性的条件，然后将其应用于推导反例。 AI

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Hugging Face Daily Papers TIER_1 English(EN) · 2026-09-09 17:26

Rockafellar约束条件下，极大单调算子的非极大值和

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…