A characterization of the extended best φ-approximation operator

Abstract

Given an non necessarily linear operator T defined from an Orlicz space L φ′(Ω, , μ) into itself, where φ′ denote the derivative of a strictly convex function φ, we give necessary and sufficient conditions on T assuring that this operator is an extended best φ-approximation operator given a suitable σ-lattice ℒ ⊆ .