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

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 ${\mathbf{J}}^{\ast }$, or $c_0$ or its dual ${\ell }^1$, admits a non type (D) operator.

34 pages

References in corpus (1)

• Maximal monotone operators with a unique extension to the bidual