Lucus Brady | Searcharxiv

arXiv2026

A Hilbert Module Approach to Classical and Quantum Reference Frames

In this paper, we present a model for classical and quantum reference frames for $C^*$-algebras by utilizing Hilbert modules and equivariant correspondences of $C^*$-dynamical systems. We show the classical model provides a commutative baseline for the quantum model, and we discuss how the quantum model encodes the Hilbert space operational formulation of quantum reference frames. We also include various explicit examples for both classical and quantum reference frames.

math.OA↗

arXiv2026

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

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.

math.OA↗