Geometric Aspects of C^*-Extreme Points II

@misc{hotwani2026geometric,
  title = {{Geometric Aspects of $C^*$-Extreme Points II}},
  author = {Neha Hotwani},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.03563},
  eprint = {2611.03563},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.03563},
}

TY  - UNPB
TI  - Geometric Aspects of C^*-Extreme Points II
AU  - Neha Hotwani
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.03563
UR  - https://arxiv.org/abs/2611.03563
AB  - Building on the results of \cite{HR}, we investigate the relationship between C^*-extremality and linear extremality in the closed unit balls of general unital C^*-algebras. We show that, unlike in von Neumann algebras, these two notions of extremality need not coincide in general C^*-algebras. More precisely, we prove that the unilateral shift is a linear extreme point, but not a C^*-extreme point, of the closed unit ball of the Toeplitz C^*-algebra. We further establish that C^*-extremality implies linear extremality whenever the C^*-algebra admits a faithful unital representation on a separable Hilbert space. We also prove this implication for elements admitting a factorization x=v|x|, where v is a partial isometry belonging to the algebra, and extend the result to suitable quotient C^*-algebras, including the Calkin algebra. Finally, we characterize the linear extreme points of the closed unit ball of unital C^*-subalgebras of B(H) containing the compact operators.
ER  -