On Approximate Birkhoff-James Orthogonality and Approximate *-orthogonality in C*-algebras

We offer a new de nition of ε-orthogonality in normed spaces, and we try to explain some properties of which. Also we introduce some types of ε-orthogonality in an arbitrary C * -algebra A, as a Hilbert C * -module over itself, and investigate some of its properties in such spaces. We state some results relating range- kernel orthogonality in C * -algebras.