Angle preserving property for a pair of mappings

Abstract

We investigate the approximate angle preserving property for a pair of linear mappings defined between normed spaces. Initially, we focus on mappings defined between real inner product spaces. We establish a relationship between mappings that satisfy such a property. We then bring the topics to Hilbert C ^∗ - modules, and provide a characterization for such a pair of mappings. Finally, we consider the pair of mappings defined between normed spaces. The notion of angle that we consider in normed spaces is one that preserves isosceles orthogonality.