Order Isomorphisms on Order Intervals of Atomic JBW-Algebras

Springer Science and Business Media LLC - Tập 92 - Trang 1-20 - 2020
Mark Roelands1, Marten Wortel2
1School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, UK
2Department of Mathematics and Applied Mathematics, University of Pretoria, Hatfield, Pretoria, South Africa

Tóm tắt

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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Springer Science and Business Media LLC

Tập 92

1-20

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