论文标题
频谱截断状态空间的Gromov-Hausdorff收敛
Gromov-Hausdorff convergence of state spaces for spectral truncations
论文作者
论文摘要
我们研究了度量的收敛方面在几何频谱截断上。我们发现了操作员系统光谱序列序列的一般条件，这些条件允许人们在配备Connes的距离公式时证明相应状态空间的Gromov-Hausdorff收敛性。我们为圆的光谱截断，圆上的光谱截断，具有有限数量的傅立叶模式，以及收敛到球体的矩阵代数。
We study the convergence aspects of the metric on spectral truncations of geometry. We find general conditions on sequences of operator system spectral triples that allows one to prove a result on Gromov-Hausdorff convergence of the corresponding state spaces when equipped with Connes' distance formula. We exemplify this result for spectral truncations of the circle, Fourier series on the circle with a finite number of Fourier modes, and matrix algebras that converge to the sphere.
