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arXiv · 2005.08544

Gromov-Hausdorff convergence of state spaces for spectral truncations

Walter D. van Suijlekom
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Abstract

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.

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BibTeXRIS

Walter D. van Suijlekom. 2020-05-18. Gromov-Hausdorff convergence of state spaces for spectral truncations. https://doi.org/10.1016/j.geomphys.2020.104075

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