A New Qualification Condition for the Maximality of the Sum of Maximal Monotone Operators in General Banach Spaces

Maicon Marques Alves; Benar Fux Svaiter

Abstract

We study maximal monotonicity of the sum of maximal monotone operators in general Banach spaces. Under certain qualification condition (QC) on the domain of Fitzpatrick convex representations of the operators the sum is maximal monotone, even in nonreflexive Banach spaces.

Author information

Contact details are reproduced from the original publication and may be historical.

Maicon Marques Alves

Dep. de Matemática, Universidade Federal de Santa Catarina, 88040-900 Florianópolis, Brazil

maicon@impa.br

Benar Fux Svaiter

Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Jardim Botânico, Rio de Janeiro, RJ 22460-320, Brazil

benar@impa.br

Keywords

Maximal monotone operators
sum
nonreflexive Banach spaces
Fitzpatrick functions

Mathematics Subject Classification

47H05, 49J52, 47N10

Suggested citation

M. Marques Alves, B. F. Svaiter. “A New Qualification Condition for the Maximality of the Sum of Maximal Monotone Operators in General Banach Spaces.” Journal of Convex Analysis 19 (2012), No. 2, 575–589.