Non‐commutative peaking phenomena and a local version of the hyperrigidity conjecture

@article{Clouatre2017NoncommutativePP,
  title={Non‐commutative peaking phenomena and a local version of the hyperrigidity conjecture},
  author={Raphael Clouatre},
  journal={Proceedings of the London Mathematical Society},
  year={2017},
  volume={117}
}
  • Raphael Clouatre
  • Published 6 September 2017
  • Mathematics
  • Proceedings of the London Mathematical Society
We investigate various notions of peaking behaviour for states on a C∗ ‐algebra, where the peaking occurs within an operator system. We pay particularly close attention to the existence of sequences of elements forming an approximation of the characteristic function of a point in the state space. We exploit such characteristic sequences to localise the C∗ ‐algebra at a given state, and use this localisation procedure to verify a variation of Arveson's hyperrigidity conjecture for arbitrary… 
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