Maximal monotonicity, conjugation and the duality product in non-reflexive Banach spaces

2008/09/23 by M. Marques Alves, B. F. Svaiter, Alves, M. Marques +1 · 1 citation
Computer Science · Mathematics · #47H05 #47N10. #49J52 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Inequalities and Applications #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.0809.3911

openalex publication_date 2008/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Maximal monotone operators on a Banach space into its dual can be represented by convex functions bounded below by the duality product. It is natural to ask under which conditions a convex function represents a maximal monotone operator. A satisfactory answer, in the context of reflexive Banach spaces, has been obtained some years ago. Recently, a partial result on non-reflexive Banach spaces was obtained. In this work we study some others conditions which guarantee that a convex function represents a maximal monotone operator in non-reflexive Banach spaces.

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• Geometric properties of maximal monotone operators and convex functions which may represent them

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