An orthogonality in normed linear spaces based on angular distance inequality

Abstract

In this paper, we present a new orthogonality in a normed linear space which is based on an angular distance inequality. Some properties of this orthogonality are discussed. We also find a new approach to the Singer orthogonality in terms of an angular distance inequality. Some related geometric properties of normed linear spaces are discussed. Finally a characterization of inner product spaces is obtained.Mathematics Subject Classification. Primary 46B20; Secondary 47A30.

Homogeneity of isosceles orthogonality, transitivity of the norm, and characterizations of inner product spaces

“…Remark 5. In [7], F. Dadipour et al remarked that a detail in the proof of Lemma 5 in [10] is not clear. Namely, that for a point u ∈ H X and a point z satisfying u ⊥ I z, the existence of a decreasing sequence {γ n } +∞ n=1 converging to 0, and satisfying…”