On sum of range sets of sum of two maximal monotone operators

In the setting of non-reflexive spaces (Grothendieck Banach spaces), we establish (۱) \overline{ran (A+B)}=\overline{ran A+ran B}(۲) int (ran (A+B))=int(ran A+ran B).with the assumption that A is a maximal monotone operator and B is a single-valued maximal monotone operator such that A+B is ultramaximally monotone. Conditions (۱) and (۲) are known as Br\acute{e}zis-Haraux conditions.

کلیدواژه ها:

monotone operator ، Maximal Monotone Operator ، Ultramaximal Monotone Operator ، Bracute{e}zis-Haraux conditions