On some aspects of orthogonality in the context of C*-algebras

The purpose of the report is to demonstrate some new perspective on maps in C*-algebras equipped with an orthogonality relation. Sets of partial isometries in C*-algebras with *-order and *-orthogonality are investigated and the Jordan*-isomorphism of AW*-algebras is studied from the point of view of description in terms of ordered sets of partial isometries. In addition, the concept of algebraic *-orthogonality of maps between C*-algebras is investigated, as well as the concept of range-orthogonality on various structures.