Order isomorphisms on order intervals of atomic JBW-algebras

2019/11/09 by Roelands, Mark, Wortel, Marten · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1911.03742

Abstract

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.

Cited by

• Identifying JBW^*-algebras through their spheres of positive elements

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• Order theoretical structures in atomic JBW-algebras: disjointness, bands, and centres
• On order automorphisms of the effect algebra
• Sharp and principal elements in effect algebras
• Identifying JBW^*-algebras through their spheres of positive elements