Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Faithfulness of bifree product states


Author: Christopher Ramsey
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 46L30, 46L54, 46L09
DOI: https://doi.org/10.1090/proc/14194
Published electronically: August 10, 2018
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Given a nontrivial family of pairs of faces of unital $ \mathrm {C}^*$-algebras where each pair has a faithful state, it is proved that if the bifree product state is faithful on the reduced bifree product of this family of pairs of faces, then each pair of faces arises as a minimal tensor product. A partial converse is also obtained.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 46L30, 46L54, 46L09

Retrieve articles in all journals with MSC (2010): 46L30, 46L54, 46L09


Additional Information

Christopher Ramsey
Affiliation: Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada
Address at time of publication: Department of Mathematics and Statistics, MacEwan University, Edmonton, Alberta, Canada
Email: Ramseyc5@macewan.ca

DOI: https://doi.org/10.1090/proc/14194
Keywords: Free probability, operator algebras, bifree
Received by editor(s): September 19, 2017
Received by editor(s) in revised form: March 27, 2018, and April 17, 2018
Published electronically: August 10, 2018
Communicated by: Adrian Ioana
Article copyright: © Copyright 2018 American Mathematical Society

American Mathematical Society