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PreprintarXiv licencearXiv

UCP Maps on Finite Toeplitz Systems

  • Ritul Duhan
  • Abhay Jindal
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Abstract

We study unital completely positive (UCP) maps on the finite Toeplitz operator system 𝒯d of d Γ— d Toeplitz matrices. We give an explicit characterization of pure UCP maps on 𝒯d taking values in Mn in terms of positive nΓ— n matrix-valued trigonometric polynomials of degree at most dβˆ’1. This characterization yields a checkable criterion for deciding whether a given UCP map is pure. As an application, we prove that every pure UCP map on 𝒯d has a unique completely positive extension to the generated C*-algebra.

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Cite

BibTeXRIS
BibTeX
@misc{duhan2026maps,
  title = {{UCP Maps on Finite Toeplitz Systems}},
  author = {Ritul Duhan and Abhay Jindal},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.02561},
  eprint = {2606.02561},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.02561},
}
RIS
TY  - UNPB
TI  - UCP Maps on Finite Toeplitz Systems
AU  - Ritul Duhan
AU  - Abhay Jindal
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2606.02561
UR  - https://arxiv.org/abs/2606.02561
AB  - We study unital completely positive (UCP) maps on the finite Toeplitz operator system 𝒯_d of d Γ— d Toeplitz matrices. We give an explicit characterization of pure UCP maps on 𝒯_d taking values in M_n in terms of positive nΓ— n matrix-valued trigonometric polynomials of degree at most dβˆ’1. This characterization yields a checkable criterion for deciding whether a given UCP map is pure. As an application, we prove that every pure UCP map on 𝒯_d has a unique completely positive extension to the generated C^*-algebra.
ER  -