Metrics on states from actions of compact groups
Abstract
Let a compact Lie group act ergodically on a unital $C^*$algebra $A$. We consider several ways of using this structure to define metrics on the state space of $A$. These ways involve length functions, norms on the Lie algebra, and Dirac operators. The main thrust is to verify that the corresponding metric topologies on the state space agree with the weak$*$ topology.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 July 1998
 DOI:
 10.48550/arXiv.math/9807084
 arXiv:
 arXiv:math/9807084
 Bibcode:
 1998math......7084R
 Keywords:

 Operator Algebras;
 46L87 (primary) 58B30;
 60B10 (secondary)
 EPrint:
 Publication version. Very minor corrections. 20 pages AMSTEX