Symmetrized strong Birkhoff–James orthogonality in C*-algebras

In this talk we present some results on 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 a 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. This is a joint work with A. Guterman, B. Kuzma, R. Rajić and S. Zhilina.