Spectral Truncations in Noncommutative Geometry and Operator Systems

@article{Connes2020SpectralTI,
  title={Spectral Truncations in Noncommutative Geometry and Operator Systems},
  author={Alain Connes and Walter D. van Suijlekom},
  journal={arXiv: Quantum Algebra},
  year={2020}
}
In this paper we extend the traditional framework of noncommutative geometry in order to deal with spectral truncations of geometric spaces (i.e. imposing an ultraviolet cutoff in momentum space) and with tolerance relations which provide a coarse grain approximation of geometric spaces at a finite resolution. In our new approach the traditional role played by $C^*$-algebras is taken over by operator systems. As part of the techniques we treat $C^*$-envelopes, dual operator systems and stable… 
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  • A. Connes, H. Moscovici
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    Proceedings of the National Academy of Sciences of the United States of America
  • 2022
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