A strong version of the Birkhoff-James orthogonality in Hilbert C*-modules

In this paper we introduce a strong version of the Birkhoff–James orthogonality in Hilbert C*- modules. We show that this relation can be described as the Birkhoff–James orthogonality of appropriate elements of V, and characterized in terms of states acting on the underlying C*- algebra A. Some analogous relations of this type are considered as well.