  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 Br{\o}nsted-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.
