J* E* C* N* U* N* S* ›› 2025, Vol. 2025 ›› Issue (6): 14-18.doi: 10.3969/j.issn.1000-5641.2025.06.002

Previous Articles     Next Articles

Finiteness and boundedness of metrics on state spaces

Botao LONG1(), Wentao SHEN1, Yueliang LIANG2   

  1. 1. School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
    2. School of Mathematics, North University of China, Taiyuan 030051, China
  • Received:2024-03-27 Online:2025-11-25 Published:2025-11-29

Abstract:

We provide a sufficient condition under which the finiteness and boundedness of metrics, as defined by Rieffel within the framework of Banach spaces, are equivalent. Additionally, we characterize the boundedness of metrics on the state spaces of $C^*{\text{-}} $algebras from multiple perspectives.

Key words: state space, metric, finiteness, boundedness

CLC Number: