New results for best approximation on Banach lattices Original Research Article

The purpose of this paper is to introduce and to discuss the concept of approximation preserving operators on Banach lattices with a strong unit. We show that every lattice isomorphism is an approximation preserving operator. Also we give a necessary and sufficient condition for uniqueness of the best approximation by closed normal subsets of X+X+, and show that this condition is characterized by some special operators.