Unitary groups, Ktheory and traces
Abstract
We show that continuous group homomorphisms between unitary groups of unital C*algebras induce maps between spaces of continuous realvalued affine functions on the trace simplices. Under certain $K$theoretic regularity conditions, these maps can be seen to commute with the pairing between $K_0$ and traces. If the homomorphism is contractive and sends the unit circle to the unit circle, the map between spaces of continuous realvalued affine functions can further be shown to be unital and positive (up to a minus sign).
 Publication:

arXiv eprints
 Pub Date:
 May 2023
 DOI:
 10.48550/arXiv.2305.15989
 arXiv:
 arXiv:2305.15989
 Bibcode:
 2023arXiv230515989S
 Keywords:

 Mathematics  Operator Algebras;
 46L35 (Primary);
 46L80 (Secondary)
 EPrint:
 accepted version, to appear in Glasgow Mathematics Journal