We show that Connes' metric on the state space associated with a spectral triple is nowhere infinite exactly when it is globally bounded. Moreover, we produce a family of simple examples showing that this is not automatically the case.
Bibliografisk noteFunding Information:
The authors gratefully acknowledge the financial support from the Independent Research Fund Denmark through grant no. 9040‐00107B and 1026‐00371B, and from ERC through the MSCA Staff Exchanges grant no. 101086394. Moreover, they are grateful to Erik Christensen and Jens Kaad for many illuminating discussions on matters related to metrics on state spaces, to Max Holst Mikkelsen for pointing out an inaccuracy in a preliminary version of the paper, to Pierre Martinetti and Jean‐Christophe Wallet for making them aware of the references [ 3 ] and [ 16 ] and to the anonymous referee for helpful clarifications.
© 2023 The Author(s). The Bulletin of the London Mathematical Society is copyright © London Mathematical Society.