Characterization of Best Approximation Points with Lattice Homomorphisms

In this paper we prove some characterization theoremsin the theory of best approximation in banach lattices. we use a newidea for finding the best approximation points in an ideal. we find thedistance between an ideal i and an element x by using lattice homomorphisms.we introduce maximal ideals of an am space and characterizeother ideals by the maximal ideals. we also give a new representationfor principle ideals in banach lattices that is a majorizing subspace andwe show that these principle ideals are proximinal. the role of latticehomomorphisms in this paper is very important.