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arXiv · 1108.1463

Construction of pathological maximally monotone operators on non-reflexive Banach spaces

Heinz H. Bauschke·Jonathan M. Borwein·Xianfu Wang·Liangjin Yao
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Abstract

In this paper, we construct maximally monotone operators that are not of Gossez's dense-type (D) in many nonreflexive spaces. Many of these operators also fail to possess the Brønsted-Rockafellar (BR) property. Using these operators, we show that the partial inf-convolution of two BC--functions will not always be a BC--function. This provides a negative answer to a challenging question posed by Stephen Simons. Among other consequences, we deduce that every Banach space which contains an isomorphic copy of the James space $\mathbf{J}$ or its dual $\mathbf{J}^*$, or $c_0$ or its dual $\ell^1$, admits a non type (D) operator.

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Heinz H. Bauschke, Jonathan M. Borwein, Xianfu Wang, Liangjin Yao. 2011-08-06. Construction of pathological maximally monotone operators on non-reflexive Banach spaces. https://arxiv.org/abs/1108.1463

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