Back to Search
Start Over
Concavity of certain matrix trace and norm functions. II.
- Source :
-
Linear Algebra & its Applications . May2016, Vol. 496, p193-220. 28p. - Publication Year :
- 2016
-
Abstract
- We refine Epstein's method to prove joint concavity/convexity of matrix trace functions of Lieb type Tr f ( Φ ( A p ) 1 / 2 Ψ ( B q ) Φ ( A p ) 1 / 2 ) and symmetric (anti-) norm functions of the form ‖ f ( Φ ( A p ) σ Ψ ( B q ) ) ‖ , where Φ and Ψ are positive linear maps, σ is an operator mean, and f ( x γ ) with a certain power γ is an operator monotone function on ( 0 , ∞ ) . Moreover, the variational method of Carlen, Frank and Lieb is extended to general non-decreasing convex/concave functions on ( 0 , ∞ ) so that we prove joint concavity/convexity of more trace functions of Lieb type. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 496
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 113408170
- Full Text :
- https://doi.org/10.1016/j.laa.2015.12.032