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A Characterization of the Extended Best φ-Approximation Operator

Given an non necessarily linear operator T defined from an Orlicz space L φ′(Ω, 𝒜, 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 ⊆ 𝒜.