On symmetry of Birkhoff orthogonality in the positive cones of C⁎-algebras with applications

Abstract

Abstract In this paper, local symmetry of Birkhoff orthogonality is considered in the positive cones of C ⁎ -algebras. For the positive cone A + of a C ⁎ -algebra A , the notion of A + -local left (or right) symmetric points for Birkhoff orthogonality is introduced. Some simple characterizations of them are given. As an application, we determine the form of Birkhoff orthogonality preservers between the positive cones of C ⁎ -algebras by using Jordan ⁎-isomorphisms.