Inherited Properties of Effect Algebras Preserved by Isomorphisms

Abstract

We show that isomorphism of effect algebras preserves properties of effect algebras derived from effect algebraic sum ? of elements. These are partial order, order convergence, order topology, existence of states and other important properties. However, there are properties of effect algebras for which the preservation of the ?-operation is not substantial and they need not be preserved.

Keywords

• effect algebras
• operator effect algebras
• isomorphisms
• operator representations of effect algebras