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arXiv · 2312.08215

Images of Order Zero Maps

Kristin Courtney·Wilhelm Winter
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Abstract

We give sufficient conditions allowing one to build a C*-algebraic structure on a self-adjoint linear subspace of a C*-algebra in such a way that the subspace is naturally identified with the resulting C*-algebra via a completely positive order zero map. This leads to necessary and sufficient conditions to realize a self-adjoint linear subspace of a C*-algebra as the image of an order zero map from a C*-algebra and to determine whether it is completely order isomorphic to a C*-algebra via an order zero map.

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Kristin Courtney, Wilhelm Winter. 2023-12-13. Images of Order Zero Maps. https://arxiv.org/abs/2312.08215

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