Year: 2026
Type: preprint
Abstract: We study unital completely positive (UCP) maps on the finite Toeplitz operator system $\mathcal T_d$ of $d \times d$ Toeplitz matrices. We give an explicit characterization of pure UCP maps on $\mathcal T_d$ taking values in $M_n$ in terms of positive $n\times n$ matrix-valued trigonometric polynomials of degree at most $d-1$. 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 $\mathcal T_d$ has a unique completely positive extension to the generated $C^*$-algebra.
Source: arXiv (Cornell University)
Authors: Duhan, Ritul, Jindal, Abhay
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7163133715