## Abstract and Applied Analysis

### Extension of The Best Approximation Operator in Orlicz Spaces

#### Abstract

Let $(\Omega{},\mathcal{A},\mu{})$ be a probability space and $\mathcal{L}\subset{}\mathcal{A}$ a sub-$\sigma{}$-lattice of the $\sigma{}$-algebra $\mathcal{A}$. We study an extension of the best $\phi{}$-approximation operator from an Orlicz space ${L}^{\phi{}}$ to the space ${L}^{{\phi{}}^{\prime{}}}$, where ${\phi{}}^{\prime{}}$ denotes the derivative of the convex, but not necessarily a strictly convex function $\phi{}$. We obtain convergence results when a sequence of $\sigma{}$-algebras ${\mathcal{B}}_{\text{n}}$ converges to ${\mathcal{B}}_{\infty{}}$ in a suitable way.

#### Article information

Source
Abstr. Appl. Anal., Volume 2008 (2008), Article ID 374742, 15 pages.

Dates
First available in Project Euclid: 9 September 2008

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1220969155

Digital Object Identifier
doi:10.1155/2008/374742

Mathematical Reviews number (MathSciNet)
MR2393120

Zentralblatt MATH identifier
1160.41308

#### Citation

Carrizo, Ivana; Favier, Sergio; Zó, Felipe. Extension of The Best Approximation Operator in Orlicz Spaces. Abstr. Appl. Anal. 2008 (2008), Article ID 374742, 15 pages. doi:10.1155/2008/374742. https://projecteuclid.org/euclid.aaa/1220969155

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