A CHARACTERIZATION OF SIMULTANEOUS ORTHOGONALITY IN COMPLETE LATTICE BANACH SPACES

We consider the notion of orthogonality introduced by Birkhoff. Note that, there are also other notions of orthogonality in normed linear spaces which are the extensions of the usual notion of orthogonality in Hilbert spaces and apply the problems of the best simultaneous approximation for closed convex sets in a conditionally complete lattice Banach space X with the strong unit 1: The concept of "¡orthogonality was introduced by vaezpour, and we introduced the concept of simultaneous orthogonality. In this paper, we will consider the relation between these concepts and the dual of X: