Approximate Birkhoff orthogonalities in normed spaces

Abstract

In a normed space we characterize the approximate orthogonality in terms of extreme points of the closed unit ball in dual space. There is also another (and older) definition of an approximate orthogonality and therefore in this paper both approximate orthogonalities are compared. Moreover, we characterize the approximate orthogonality in the class of compact operators on a reflexive Banach space.