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Extension of The Best Approximation Operator in Orlicz Spaces

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Listed:
  • Ivana Carrizo
  • Sergio Favier
  • Felipe Zó

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.

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Handle: RePEc:wly:jnlaaa:v:2008:y:2008:i:1:n:374742
DOI: 10.1155/2008/374742
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