Linear mappings approximately preserving orthogonality

We consider the class of linear mappings, between real or complex inner product spaces, such that for each two orthogonal vectors in the domain their values are ɛ-orthogonal in the target space. By ɛ-orthogonality (0⩽ɛ<1) we mean the relation u⊥ɛv⇔|〈u|v〉|⩽ɛ‖u‖‖v‖.