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arXiv · 2605.08004

Functoriality of the KSGNS Construction for Intertwiners of Strict Positive $C^*$-Correspondences

Lucus Brady·Ryan Grady
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Abstract

We prove that the KSGNS construction can be viewed as an endofunctor on a category whose objects are positive $C^*$-correspondences from a fixed $C^*$-algebra and morphisms are given by intertwiners which account for automorphisms of the fixed $C^*$-algebra. Using this perspective, we provide a functorial perspective for strict positive equivariant $C^*$-correspondences of $C^*$-dynamical systems and show every strict positive equivariant $C^*$-correspondence of $C^*$-dynamical systems unitarily uniquely dilates under the KSGNS construction to an equivariant $C^*$-correspondence of the dynamical systems.

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BibTeXRIS

Lucus Brady, Ryan Grady. 2026-05-08. Functoriality of the KSGNS Construction for Intertwiners of Strict Positive $C^*$-Correspondences. https://arxiv.org/abs/2605.08004

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