The Sum and Chain Rules for Maximal Monotone Operators

2006/09/11 by M. D. Voisei, Voisei, M. D.
Computer Science · Mathematics · #46N10 #47H05 #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.math/0609296

openalex publication_date 2006/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is primarily concerned with the problem of maximality for the sum A+B and composition L^*ML in non-reflexive Banach space settings under qualifications constraints involving the domains of A,B,M. Here X, Y are Banach spaces with duals X^*, Y^*, A,B:X\rightrightarrows X^*, M:Y\rightrightarrows Y^* are multi-valued maximal monotone operators, and L:X→ Y is linear bounded. Based on the Fitzpatrick function, new characterizations for the maximality of an operator as well as simpler proofs, improvements of previously known results, and several new results on the topic are presented.

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