Vector valued continuous function spaces as C^∗-algebras

@misc{hotwani2026vector,
  title = {{Vector valued continuous function spaces as $C^\ast$-algebras}},
  author = {Neha Hotwani and T. S. S. R. K. Rao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.02680},
  eprint = {2609.02680},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.02680},
}

TY  - UNPB
TI  - Vector valued continuous function spaces as C^∗-algebras
AU  - Neha Hotwani
AU  - T. S. S. R. K. Rao
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2609.02680
UR  - https://arxiv.org/abs/2609.02680
AB  - Let Ω be a compact Hausdorff space, and let cA be a unital C^*-algebra. In this study, we continue our examination of the comparison between C^*-extreme points and linear extremal structures of the unit ball, in the vector-valued C^*-algebra C(Ω, cA), building upon the work initiated in \cite{HR}. We first enlarge the class of C^∗-algebras in which a $ C^\ast$-extreme point is an extreme point. We demonstrate that if cA has a faithful tracial state, then any C^*-extreme point of the unit ball C(Ω, cA)_1 is a unitary. Additionally, we identify a classes of C^*-algebras where the concepts of C^*-extreme and pointwise C^*-extreme points in C(Ω, cA)_1 coincide. We show this holds if a von Neumann algebra has a separable predual with the Radon-Nikodým property.
ER  -