From norm derivatives to orthogonalities in Hilbert C*-modules

Abstract

Let be a Hilbert -module over a -algebra and let be the set of states on . In this paper, we first compute the norm derivative for nonzero elements x and y of as follows: We then apply it to characterize different concepts of orthogonality in . In particular, we present a simpler proof of the classical characterization of Birkhoff–James orthogonality in Hilbert -modules. Moreover, some generalized Daugavet equation in the -algebra of all bounded linear operators acting on a Hilbert space is solved.