Intriguing maximally monotone operators derived from nonsunny nonexpansive retractions

Monotone operator theory and fixed point theory for nonexpansive mappings are central areas in modern nonlinear analysis and optimization. Although these areas are fairly well developed, almost all examples published are based on subdifferential operators, linear relations, or combinations thereof. In this paper, we construct an intriguing maximally monotone operator induced by a certain nonexpansive retraction. We analyze this operator, which does not appear to be assembled from subdifferential operators or linear relations, in some detail. Particular emphasis is placed on duality and strong monotonicity.