Gromov-Hausdorff convergence of state spaces for spectral truncations

JOURNAL OF GEOMETRY AND PHYSICS

卷:162

Article

van Suijlekom, Walter D.¹ 

[1] Radboud Univ Nijmegen, Inst Math Astrophys & Particle Phys, Heyendaalseweg 135, NL-6525 AJ Nijmegen, Netherlands

关键词: Noncommutative geometry;    Gromov-Hausdorff convergence;    Quantum metric spaces;   

DOI  :  10.1016/j.geomphys.2020.104075

来源: Elsevier

【 摘 要 】

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. (C) 2020 The Author. Published by Elsevier B.V.

【 授权许可】

Free