Abstract and Applied Analysis
Volume 2008 (2008), Article ID 374742, 15 pages
doi:10.1155/2008/374742
Extension of the best approximation operator in Orlicz spaces
Ivana Carrizo
, Sergio Favier
and Felipe Zó
Instituto de Matemática Aplicada San Luis, UNSL-CONICET, Avda, Ejército de los Andes 950, 5700 San Luis, Argentina
Abstract
Let (Ω,𝒜,μ) be a probability space and ℒ⊂𝒜 a sub-σ-lattice of the σ-algebra 𝒜. We study an extension of the best ϕ-approximation operator from an Orlicz space Lϕ to the space Lϕ′, where ϕ′ denotes the derivative of the convex, but not necessarily a strictly convex function ϕ. We obtain convergence results when a sequence of σ-algebras ℬn converges to ℬ∞ in a suitable way.