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There are several nonequivalent extensions of orthogonality from inner product spaces to general normed spaces. One of the most well-known is the Birkhoff-James orthogonality: if X is a normed space and x, y∈X then x is Birkhoff-James orthogonal to y if ‖x+λy‖≥‖x‖ for all scalars λ. In a C*-algebra A we can also discuss the case when x∈A is Birkhoff-James orthogonal to all the elements of the form ya, a∈A. In this case we say that x is strongly Birkhoff-James orthogonal to y. We discuss this kind of orthogonality in some special classes of C*-algebras. This is a joint work with A. Guterman, B. Kuzma, R. Rajić and S. Zhilina.
C*-algebra, orthogonality, Birkhoff-James orthogonality
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