Functoriality of the KSGNS Construction for Intertwiners of Strict Positive $C^*$-Correspondences
Year: 2026
Type: preprint
Abstract: We prove that the KSGNS construction can be viewed as an endofunctor on a category whose objects are strict 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.
Source: arXiv (Cornell University)
Authors: Brady, Lucus, Grady, Ryan
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7160823820