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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.
Birkhoff–James orthogonality ; state ; Hilbert C*-module ; C*-algebra
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