Operator equalities and Characterizations of Orthogonality in Pre-Hilbert $C^{\ast }$-Modules

Rasoul Eskandari, M. S. Moslehian, Dan Popovici

In the first part of the paper, we use states on $C^{\ast }$-algebras in order to establish some equivalent statements to equality in the triangle inequality, as well as to the parallelo…