Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Majorization in C*-algebras


Authors: Ping Wong Ng, Leonel Robert and Paul Skoufranis
Journal: Trans. Amer. Math. Soc. 370 (2018), 5725-5759
MSC (2010): Primary 46L05
DOI: https://doi.org/10.1090/tran/7163
Published electronically: March 16, 2018
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We investigate the closed convex hull of unitary orbits of selfadjoint elements in arbitrary unital C*-algebras. Using a notion of majorization against unbounded traces, a characterization of these closed convex hulls is obtained. Furthermore, for C*-algebras satisfying Blackadar's strict comparison of positive elements by traces or for collections of C*-algebras with a uniform bound on their nuclear dimension, an upper bound for the number of unitary conjugates in a convex combination required to approximate an element in the closed convex hull within a given error is shown to exist. This property, however, fails for certain ``badly behaved'' simple nuclear C*-algebras.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 46L05

Retrieve articles in all journals with MSC (2010): 46L05


Additional Information

Ping Wong Ng
Affiliation: Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana
Email: png@louisiana.edu

Leonel Robert
Affiliation: Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana
Email: lrobert@louisiana.edu

Paul Skoufranis
Affiliation: Department of Mathematics and Statistics, York University, Toronto, Canada
Email: pskoufra@yorku.ca

DOI: https://doi.org/10.1090/tran/7163
Received by editor(s): August 26, 2016
Received by editor(s) in revised form: December 15, 2016
Published electronically: March 16, 2018
Article copyright: © Copyright 2018 American Mathematical Society

American Mathematical Society