## Majorization in C*-algebras

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- by Ping Wong Ng, Leonel Robert and Paul Skoufranis PDF
- Trans. Amer. Math. Soc.
**370**(2018), 5725-5759 Request permission

## 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

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## Additional Information

**Ping Wong Ng**- Affiliation: Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana
- MR Author ID: 699995
- Email: png@louisiana.edu
**Leonel Robert**- Affiliation: Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana
- MR Author ID: 716339
- Email: lrobert@louisiana.edu
**Paul Skoufranis**- Affiliation: Department of Mathematics and Statistics, York University, Toronto, Canada
- MR Author ID: 966934
- Email: pskoufra@yorku.ca
- Received by editor(s): August 26, 2016
- Received by editor(s) in revised form: December 15, 2016
- Published electronically: March 16, 2018
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**370**(2018), 5725-5759 - MSC (2010): Primary 46L05
- DOI: https://doi.org/10.1090/tran/7163
- MathSciNet review: 3803146