On three concepts of orthogonality in Hilbert C*- modules

In this paper we consider three concepts of orthogonality in a Hilbert C*-module V over a C*- algebra A: the Birkhoff-James orthogonality, the strong Birkhoff-James orthogonality, and the orthogonality with respect to the A-valued inner product on V. We characterize the classes of Hilbert C*-modules in which any two of them coincide.