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arXiv · 2601.14873

Order isomorphisms in $C^*$-algebras

Youssef El Khatiri
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Abstract

We provide a complete description of the order isomorphisms between the self-adjoint parts of $C^*$-algebras. Furthermore, we characterize such isomorphisms between general operator intervals in $AW^*$-algebras. For the description, we use Jordan $^*$-isomorphisms and closed operators in the regular rings of $AW^{*}$-algebras. This work generalizes previous results on von Neumann algebras.

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Youssef El Khatiri. 2026-01-21. Order isomorphisms in $C^*$-algebras. https://arxiv.org/abs/2601.14873

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