Compressions on partially ordered abelian groups
David J. Foulis · Proceedings of the American Mathematical Society · 2004
If A A is a C*-algebra and p ∈ A p\in A is a self-adjoint idempotent, the mapping a ↦ p a p a\mapsto pap is called a compression on A A . We introduce effect-ordered rings as generalizations of unital C*-algebras and characterize compressions on these rings. The resulting characterization leads to a generalization of the notion of compression on partially ordered abelian groups with order units.