Details

Autor(en) / Beteiligte

• Roelands, Mark
• Wortel, Marten

Titel

Order Isomorphisms on Order Intervals of Atomic JBW-Algebras

Ist Teil von

• Integral equations and operator theory, 2020-08, Vol.92 (4), Article 33

Ort / Verlag

Cham: Springer International Publishing

Erscheinungsjahr

2020

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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.