The Dynamical Radius of Comparison for C*-Dynamical Systems

@misc{asadivasfi2026dynamical,
  title = {{The Dynamical Radius of Comparison for C*-Dynamical Systems}},
  author = {M. Ali Asadi-Vasfi and N. Christopher Phillips},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.30211},
  eprint = {2609.30211},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.30211},
}

TY  - UNPB
TI  - The Dynamical Radius of Comparison for C*-Dynamical Systems
AU  - M. Ali Asadi-Vasfi
AU  - N. Christopher Phillips
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.30211
UR  - https://arxiv.org/abs/2609.30211
AB  - We introduce a dynamical version rc (A, α) of the radius of comparison rc (A) of a unital C*-algebra, based on the dynamical Cuntz semigroup. We also give an intrinsic ordered semigroup definition, which agrees with rc (A, α) when A is residually stably finite, and is lower semicontinuous for equivariant direct limits with injective unital maps. We construct actions α of G = ℤ / 2 ℤ on simple unital AH~algebras for which rc (A, α) lies strictly between rc (A) and rc (A) / card (G), and actions α of a finite group G on unital C*-algebras for which rc (A, α) lies strictly between rc (A) and rc (C^* (G, A, α)). For a minimal action of a countable discrete group G on a zero dimensional compact metrizable space X, we prove that rc (C (X), α) = 0 if and only if the action has dynamical comparison as defined by Kerr. For finite group actions on simple unital stably finite C*-algebras, assuming the weak tracial Rokhlin property, we get rc (A, α) ≤ rc (A) / card (G), and assuming weak tracial strict approximate innerness, we get rc (A, α) = rc (A).
ER  -