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We characterize the class of surjective (conjugate) linear mappings from B(H) to B(H) that preserve the strong Birkhoff-James orthogonality in both directions. We also give characterizations of rank-one operators as well as coisometries in terms of the strong Birkhoff-James orthogonality.
Birkhoff-James orthogonality ; strong Birkhoff-James orthogonality ; rank-one operators ; coisometry ; linear preserver
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