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We study the relation of mutual strong Birkhoff- James orthogonality in two classical C*-algebras: the C*-algebra B(H) of all bounded linear operators on a complex Hilbert space H and the commutative, possibly nonunital, C*-algebra. With the help of the induced graph it is shown that this relation alone can characterize right invertible elements. Moreover, in the case of commutative unital C*-algebras, it can detect the existence of a point with a countable local basis in the corresponding compact Hausdorff space.
(strong) Birkhoff–James orthogonality ; C*-algebra ; Graph · Diameter ; Right invertible element
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