Differentiability of the best approximation operator

1981 ◽  
Vol 29 (4) ◽  
pp. 295-306 ◽  
Author(s):  
A. V. Kolushov
Keyword(s):  
Best Approximation ◽  
Approximation Operator ◽  
The Best Approximation

scholarly journals Extension of The Best Approximation Operator in Orlicz Spaces

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
Ivana Carrizo ◽  
Sergio Favier ◽  
Felipe Zó
Keyword(s):  
Convex Function ◽  
Orlicz Space ◽  
Best Approximation ◽  
Probability Space ◽  
Orlicz Spaces ◽  
Approximation Operator ◽  
Strictly Convex ◽  
The Best Approximation ◽  
Convergence Results

Let(Ω,𝒜,μ)be a probability space andℒ⊂𝒜a sub-σ-lattice of theσ-algebra𝒜. We study an extension of the bestϕ-approximation operator from an Orlicz spaceLϕto the spaceLϕ′, whereϕ′denotes the derivative of the convex, but not necessarily a strictly convex functionϕ. We obtain convergence results when a sequence ofσ-algebrasℬnconverges toℬ∞in a suitable way.

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