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Orthogonality in normed linear spaces can be defined in different ways. We consider two types of orthogonality in C*-algebras. The Birkhoff-James orthogonality for arbitrary elements a and b of a C*-algebra A is characterized in terms of states acting on A. A characterization of a special case of the Roberts orthogonality for elements a and e, where e is the unit in A, is obtained in terms of the Davis-Wielandt shell of a.
Birkhoff-James orthogonality ; Roberts orthogonality ; C*-algebra ; state
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