Various types of orthogonality in Hilbert C*-modules

Orthogonality in Hilbert C*-modules can be defined in different ways. We discuss and compare the orthogonality with respect to the C*-valued inner product, the Birkhoff-James orthogonality and the strong Birkhoff-James orthogonality. In particular, we characterize the classes of Hilbert C*-modules in which any two types of these orthogonalities coincide.