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arXiv · 1911.03742

Order isomorphisms on order intervals of atomic JBW-algebras

Mark Roelands·Marten Wortel
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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.

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Mark Roelands, Marten Wortel. 2019-11-09. Order isomorphisms on order intervals of atomic JBW-algebras. https://arxiv.org/abs/1911.03742

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