Abstract and Applied Analysis
Volume 2008 (2008), Article ID 374742, 15 pages
doi:10.1155/2008/374742
Research Article
Extension of The Best Approximation Operator in Orlicz Spaces
Instituto de Matemática Aplicada San Luis, UNSL-CONICET, Avda, Ejército de los Andes 950, 5700 San Luis, Argentina
Received 17 December 2007; Accepted 26 February 2008
Academic Editor: Jean-Pierre Gossez
Copyright © 2008 Ivana Carrizo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.