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PreprintarXiv licencearXiv

On the Equivalence of Linear and C* Extremality for Unital Completely Positive Maps on Commutative Real C*-algebras

  • Sriram Balasubramanian
  • Karthikeyan Thangaraj
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Abstract

Let π’œ be a unital commutative real C*-algebra and β„‹ be a finite dimensional real Hilbert space. In this article, an easily verifiable necessary and sufficient condition for a linear extreme unital completely positive (UCP) map Ξ¦:π’œ β†’ B(β„‹) to be C*-extreme, is obtained. As an application, the C*-algebras π’œ on which linear extreme UCP maps coincide with the C*-extreme ones, are classified.

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Cite

BibTeXRIS
BibTeX
@misc{balasubramanian2026equivalence,
  title = {{On the Equivalence of Linear and $C^*$ Extremality for Unital Completely Positive Maps on Commutative Real $C^*$-algebras}},
  author = {Sriram Balasubramanian and Karthikeyan Thangaraj},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.15383},
  eprint = {2611.15383},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.15383},
}
RIS
TY  - UNPB
TI  - On the Equivalence of Linear and C^* Extremality for Unital Completely Positive Maps on Commutative Real C^*-algebras
AU  - Sriram Balasubramanian
AU  - Karthikeyan Thangaraj
PY  - 2026
DA  - 2026/11/11
PB  - arXiv
DO  - 10.48550/arxiv.2611.15383
UR  - https://arxiv.org/abs/2611.15383
AB  - Let π’œ be a unital commutative real C^*-algebra and β„‹ be a finite dimensional real Hilbert space. In this article, an easily verifiable necessary and sufficient condition for a linear extreme unital completely positive (UCP) map Ξ¦:π’œ β†’ B(β„‹) to be C*-extreme, is obtained. As an application, the C^*-algebras π’œ on which linear extreme UCP maps coincide with the C^*-extreme ones, are classified.
ER  -