Functoriality of the KSGNS Construction for Intertwiners of Strict Positive $C^*$-Correspondences
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918489846972416 |
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| author | Brady, Lucus Grady, Ryan |
| author_facet | Brady, Lucus Grady, Ryan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08004 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Functoriality of the KSGNS Construction for Intertwiners of Strict Positive $C^*$-Correspondences Brady, Lucus Grady, Ryan Operator Algebras Mathematical Physics 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. |
| title | Functoriality of the KSGNS Construction for Intertwiners of Strict Positive $C^*$-Correspondences |
| topic | Operator Algebras Mathematical Physics |
| url | https://arxiv.org/abs/2605.08004 |