Finer Properties of Ultramaximally Monotone Operators on Banach Spaces

We study properties of ultramaximally monotone operators. We characterize the interior and the closure of the range of an ultramaximally monotone operator. We establish the Brezis-Haraux condition in the setting of a general Banach space. Moreover, we show that every ultramaximally monotone operator is of type (NA), which generalizes Bauschke and Simons' result.