On p-height orthogonality and characterization of inner product spaces

Abstract

In this paper, we introduce and study the concept of p-height orthogonality in real normed linear spaces. This orthogonality generalizes the well-known Singer and height orthogonalities. First, we investigate main properties of this type of orthogonality. Then, variety of examples are presented to illustrate the relationship between p-height orthogonality and other previously defined (e.g., isosceles, Singer, height and Birkhoff-James) orthogonalities. Also we investigate the existence properties of this new notion of orthogonality. In particular, α-existence property is established and some interesting bounds for the values of α are obtained. Moreover, some characterizations of inner product spaces are given in terms of p-height orthogonality and its relation with Pythagorean and Birkhoff-James orthogonalities.