Year: 2026
Type: preprint
Abstract: We investigate the operator system structure of finite Hankel matrices and its connection with complex polynomials on the real line. Using polynomial matrix spectral factorization, we establish a unital complete order isomorphism between the operator system of (n + 1) x (n + 1) Hankel matrices and the dual of the operator system of polynomials of degree at most 2n. We also show that the operator system of complex polynomials is minimal, while the Hankel operator system is maximal. As an application, we characterize positivity of block Hankel matrices with entries in a C*-algebra in terms of completely positive maps on the polynomial operator system.
Source: arXiv (Cornell University)
Authors: Sinclair, Thomas, Qiu, Shengwei
Institution: Purdue University West Lafayette
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7212634530