K-theoretic invariants of the Toeplitz operator system and its dual, and of all graph operator systems
Year: 2026
Type: preprint
Abstract: We compute $K$-theoretic invariants for several finite-dimensional operator systems. These include the Toeplitz operator system and its dual (the Fejér-Riesz operator system), as well as operator systems associated to tolerance relations, aka graph operator systems. A variety of techniques is applied, adapted to each of these cases, ranging from a generalization of Carathéodory's factorization result for block Toeplitz matrices, to Wiener-Hopf factorization and Schur complements. In most instances we find that the invariants coincide with their analogues for the $C^*$-envelope, except for the $K_1$-invariants of the Fejér-Riesz operator system.
Source: arXiv (Cornell University)
Author: van Suijlekom, Walter D.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7215126881