Spectral Truncations in Noncommutative Geometry and Operator Systems

  title={Spectral Truncations in Noncommutative Geometry and Operator Systems},
  author={Alain Connes and Walter D. van Suijlekom},
  journal={arXiv: Quantum Algebra},
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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<jats:p>In this letter, we prove that the pure state space on the <jats:inline-formula><jats:alternatives><jats:tex-math>$$n \times n$$</jats:tex-math><mml:math
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The UV prolate spectrum matches the zeros of zeta.
  • A. Connes, H. Moscovici
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 2022
SignificanceWe show that the eigenvalues of the self-adjoint extension (introduced by A.C. in 1998) of the prolate spheroidal operator reproduce the UV behavior of the squares of zeros of the Riemann
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