Roelands, MarkWortel, Marten2020-08-172020-07Roelands, M., Wortel, M. Order Isomorphisms on Order Intervals of Atomic JBW-Algebras. Integral Equations and Operator Theory 92, 33 (2020). https://doi.org/10.1007/s00020-020-02590-9.0378-620X (print)1420-8989 (online)10.1007/s00020-020-02590-9http://hdl.handle.net/2263/75762In 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.en© Springer Nature Switzerland AG 2020. The original publication is available at : http://link.springer.com/journal/20.Order isomorphismsAtomic JBW-algebrasEffect algebraPostprint Article