The Birkhoff-James orthogonality in Hilbert C*-modules

We characterize the Birkhoff-James orthogonality for elements of a Hilbert C*-module in terms of states of the underlying C*-algebra. We also show that the Birkhoff-James orthogonality in a Hilbert C*-module over a C*-algebra A, and orthogonality with respect to the A-valued inner product coincide if and only if A is isomorphic to C.