AI 中文总结
本文证明非交换n-环面谱截断的算子系统状态空间在Connes距离下Gromov-Hausdorff收敛，利用环面作用和Bochner积分构造近似序同构，并推广了经典环面情形，同时研究了截断算子系统的C*-包络和传播数。
AI 中文摘要
我们证明了与非交换$n$-环面（$n\ge 2$）的谱截断相关联的算子系统的状态空间（配备Connes距离函数）的Gromov-Hausdorff收敛。$n$-环面在非交换$n$-环面上的作用，连同Bochner积分的适当使用，使我们能够构造一个$C^1$-近似序同构，从而建立收敛性。经典环面情形的早期收敛结果[20]是我们结果的一个特例。最后，我们研究了截断算子系统的$C^*$-包络和传播数，并表明环面的截断算子系统的结构性质在变形下得以保持。
英文摘要
We prove the Gromov-Hausdorff convergence of the state spaces, equipped with Connes' distance function, of the operator systems associated with spectral truncations for noncommutative $n$-tori, $n\ge 2$. The action of the $n$-torus on the noncommutative $n$-torus, together with an appropriate use of Bochner integrals, enables us to construct an $C^1$-approximate order isomorphism that establishes the convergence. The earlier convergence result for the classical case of tori [20] follows as a special case of our result. We conclude by studying the $C^*$-envelopes and propagation numbers of the truncated operator systems and show that the structural properties of the truncated operator systems for tori persist under deformation.
Comments24 pages
