Extension of the best approximation operator in Orlicz spaces

I. CARRIZO, S. FAVIER, F. ZÓ

Abstract and Applied Analysis

Hindawi Publishing Co.

Lugar: New York; Año: 2008 vol. 2008 p. 1 - 15

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 operatorfrom an Orlicz space $L^{phi}$ to the space $L^{phi´},$ where$phi´$ denotes the derivative of the convex, but not necessarilya strictly convex function $phi.$ We obtain convergence resultswhen a sequence of $sigma$-algebras $mathcal{B}_n$ converges to$mathcal{B}_{infty}$ in a suitable way.