Star Order and Partial Isometries in C*-Algebras

Abstract

Abstract: We study the poset of partial isometries in C*-algebras endowed with the *-order and *-orthogonality. We show that this structure is a complete Jordan invariant for AW*-algebras. We prove that partial isometries in von Neumann algebras form a lower semilattice. The structures of partial isometries and projections are compared.