• Corpus ID: 7845715

Metrics on State Spaces

@article{Rieffel1999MetricsOS,
  title={Metrics on State Spaces},
  author={Marc Rieffel},
  journal={arXiv: Operator Algebras},
  year={1999}
}
  • M. Rieffel
  • Published 22 June 1999
  • Mathematics, Physics
  • arXiv: Operator Algebras
In contrast to the usual Lipschitz seminorms associated to ordinary metrics on compact spaces, we show by examples that Lipschitz seminorms on possibly non-commutative compact spaces are usually not determined by the restriction of the metric they define on the state space, to the extreme points of the state space. We characterize the Lipschitz norms which are determined by their metric on the whole state space as being those which are lower semicontinuous. We show that their domain of… 
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