The Birkhoff–James orthogonality in Hilbert C ∗-modules

Abstract: In this paper we characterize the Birkhoff–James orthogonality for elements of a Hilbert C ∗-module in terms of states of the underlying C ∗-algebra. We also show that the Birkhoff–James orthogonality in a Hilbert C ∗-module over a C ∗-algebra and orthogonality with respect to the -valued inner product coincide if and only if is isomorphic to In addition, some new results concerning the case of equality in the triangle inequality for elements of a Hilbert C ∗-module are obtained. [Copyright &y& Elsevier]