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arXiv · 2609.40028

K-theoretic invariants of the Toeplitz operator system and its dual, and of all graph operator systems

Walter D. van Suijlekom
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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.

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Walter D. van Suijlekom. 2026-09-30. K-theoretic invariants of the Toeplitz operator system and its dual, and of all graph operator systems. https://arxiv.org/abs/2609.40028

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