On Roberts orthogonality in C*-algebras

We say that the elements x and y of a complex normed space X are Roberts orthogonal if the norm of x + λy is the same as the norm of x − λy for all complex numbers λ. Let A be a unital C*- algebra with the unit e. In this talk we present results which characterize Roberts orthogonality of the unit e and an arbitrary element a of A. This is a joint work with Tomislav Berić and Rajna Rajić.