发表机构
Radboud University（拉德堡德大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文计算了Toeplitz算子系统、其对偶及图算子系统的K-理论不变量，发现多数与C*-包络一致，但Fejér-Riesz系统的K1不变量例外。
AI 中文摘要
我们计算了若干有限维算子系统的$K$-理论不变量。这些系统包括Toeplitz算子系统及其对偶（Fejér-Riesz算子系统），以及与容差关系相关的算子系统，即图算子系统。针对每种情况，我们应用了多种技术，包括Carathéodory因子分解结果对块Toeplitz矩阵的推广、Wiener-Hopf因子分解和Schur补。在大多数情况下，我们发现这些不变量与其$C^*$-包络的对应不变量一致，但Fejér-Riesz算子系统的$K_1$-不变量除外。
英文摘要
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.
Comments22 pages
