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

@misc{brady2026functoriality,
  title = {{Functoriality of the KSGNS Construction for Intertwiners of Strict Positive $C^*$-Correspondences}},
  author = {Lucus Brady and Ryan Grady},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.08004},
  eprint = {2605.08004},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.08004},
}

TY  - UNPB
TI  - Functoriality of the KSGNS Construction for Intertwiners of Strict Positive C^*-Correspondences
AU  - Lucus Brady
AU  - Ryan Grady
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2605.08004
UR  - https://arxiv.org/abs/2605.08004
AB  - 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.
ER  -