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

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.