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arXiv · 1903.05302

Isometries of absolute order unit spaces

Anil Kumar Karn·Amit kumar
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Abstract

We prove that for a bijective, unital, linear map between absolute order unit spaces is an isometry if, and only if, it is absolute value preserving. We deduce that, on (unital) $JB$-algebras, such maps are precisely Jordan isomorphisms. Next, we introduce the notions of absolutely matrix ordered spaces and absolute matrix order unit spaces and prove that for a bijective, unital, linear map between absolute matrix order unit spaces is a complete isometry if, and only if, it is completely absolute value preserving. We obtain that on (unital) C$^*$-algebras such maps are precisely C$^*$-algebra isomorphism.

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Anil Kumar Karn, Amit kumar. 2019-03-13. Isometries of absolute order unit spaces. https://arxiv.org/abs/1903.05302

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