Order isomorphisms in $C^*$-algebras
Youssef El Khatiri

TL;DR
This paper characterizes order isomorphisms between self-adjoint parts of $C^*$-algebras and operator intervals in $AW^*$-algebras, extending prior results on von Neumann algebras using Jordan $^*$-isomorphisms.
Contribution
It provides a complete description of order isomorphisms in $C^*$-algebras and $AW^*$-algebras, generalizing previous work on von Neumann algebras.
Findings
Characterization of order isomorphisms using Jordan $^*$-isomorphisms.
Extension of results to general operator intervals in $AW^*$-algebras.
Generalization of known results from von Neumann algebras.
Abstract
We provide a complete description of the order isomorphisms between the self-adjoint parts of -algebras. Furthermore, we characterize such isomorphisms between general operator intervals in -algebras. For the description, we use Jordan -isomorphisms and closed operators in the regular rings of -algebras. This work generalizes previous results on von Neumann algebras.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Banach Space Theory · Holomorphic and Operator Theory
