PreprintCC BY 4.0arXiv
K-theoretic invariants of the Toeplitz operator system and its dual, and of all graph operator systems
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 K1-invariants of the Fejér-Riesz operator system.
Related
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BibTeX
@misc{suijlekom2026ktheoretic,
title = {{K-theoretic invariants of the Toeplitz operator system and its dual, and of all graph operator systems}},
author = {Walter D. van Suijlekom},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.40028},
eprint = {2609.40028},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40028},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - K-theoretic invariants of the Toeplitz operator system and its dual, and of all graph operator systems
AU - Walter D. van Suijlekom
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.40028
UR - https://arxiv.org/abs/2609.40028
AB - 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.
ER -