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

نویسندگان
Pradhan, Dillip Kumar ID 1
Pattanaik, Suvendu Ranjan ID 2

1 Department of Mathematics, National Institute of Technology, Rourkela, India

2 Department of Mathematics, National Institute of Technology, Rourkela, India

doi
10.22075/ijnaa.2019.12171.1615
چکیده

In the setting of non-reflexive spaces (Grothendieck Banach spaces), we establish (1) $\overline{ran (A+B)}=\overline{ran A+ran B}$(2) 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 (1) and (2) are known as Br$\acute{e}$zis-Haraux conditions.

کلیدواژه‌ها
monotone operator, Maximal Monotone Operator, Ultramaximal Monotone Operator, Br$acute{e}$zis-Haraux conditions