Birkhoff-James and Roberts orthogonality in C*- algebras

Two vectors in an inner product space are orthogonal if their inner product is 0. There are many different ways how the notion of orthogonality can be generalized to the class of normed spaces. Among them, the Birkhoff--James orthogonality and the Roberts orthogonality are the most important. In this talk we shall present some basic results about these two types of orthogonality. Also, we shall present some characterizations in $C^*$- algebras which are normed spaces with some additional structures. This is a joint work with Rajna Rajić and Tomislav Berić.