α,β,γ-Orthogonality

Abstract

Orthogonality in inner product spaces can be expresed using the notion of norms. So many generalization of the concept of orthogonality was made in the context of Banach spaces. In this paper we introduce a new orthogonality relation in normed linear spaces, called α,β,γ-orthogonality wich generalised most of the known orthogonality. It is shown that α,β,γ-orthogonality is homogeneus if and only if the space is a real inner product space.

Key words and phrases. (α,β)-orthogonality, (α,β,γ)-orthogonality, Pythagorean orthogonality, isosceles orthogonality, normed linear spaces, inner product spaces.

2000 Mathematics Subject Classification. Primary: 46C05 , Secondary: 51F20