In this paper a full description of order isomorphisms between effect
algebras of atomic JBW-algebras is given. We will derive a closed formula for
the order isomorphisms on the effect algebra of type I factors by proving that
the invertible part of the effect algebra of a type I factor is left invariant.
This yields an order isomorphism on the whole cone, for which a
characterisation exists. Furthermore, we will show that the obtained formula
for the order isomorphism on the invertible part can be extended to the whole
effect algebra again. As atomic JBW-algebras are direct sums of type I factors
and order isomorphisms factor through the direct sum decomposition, this yields
the desired description.Comment: 17 page
