A remark on the Brézis–Browder theorem in finite dimensional spaces

Abstract

Brézis and Browder gave an important characterization of maximal monotonicity for linear operators, in reflexive Banach spaces. In this paper, we show that this characterization also preserves the maximal p-monotonicity, in finite dimensional spaces.

Keywords:

• Maximal monotonicity
• cyclic monotonicity
• adjoint operator
• linear operator

Acknowledgements

We would like to thank the anonymous referee for the suggestions, which helped to improve this work.

Notes

No potential conflict of interest was reported by the authors.