On the Uniqueness of Reserving Pythagorean Orthogonality in Terms of Non-zero Linear Operators

Abstract

This paper is concerned with the connection between reserving Birkhoff-James orthogonality and the new particular case of the Carlsson orthogonality concerning non-zero linear operators in a complete normed linear space. The purpose of this article is to find the interrelation between reserving Pytharegorean and Birkhoff-James orthogonality. It is proved that if a non-zero linear operator reserves Pythagorean orthogonality, then it also reserves Birkhoff ’s orthogonality. It has also been proved that the unique property of orthogonality concerning the reserving Pythagorean orthogonality.