Approximate Orthogonal Preserving Mappings  on C*-Semi-inner Product Space

Murtala Umar; Abor I. Garba

doi:10.4314/cajost.v3i2.75

Approximate Orthogonal Preserving Mappings on C*-Semi-inner Product Space

Authors

Murtala Umar Department of Mathematics, Sokoto State University, Sokoto, P.M.B 2134, Sokoto State, Nigeria
Abor I. Garba Usmanu Danfodiyo University, Sokoto, P.M.B 2346, Sokoto State, Nigeria

DOI:

https://doi.org/10.4314/cajost.v3i2.75

Keywords:

C* -semi-inner product, Birkhoff-James orthogonality, Approximate orthogonality

Abstract

In this research work, we study Birkhoff-James orthogonality in an arbitrary normed linear space ^X , and establish the orthogonal preserving mapping in C ^*- semi-inner product space. It has been observed that every mapping that preserves orthogonality is necessarily a scalar multiple of an isometry. We finally introduce approximate orthogonality and investigate this notion in C^* - semi-inner product space.