Abstract
We consider trace functions (A,B) & Tr[ (Aq/2BpAq/2)s] where A and B are positive n×n matrices and ask when these functions are convex or concave. We also consider operator convexity/concavity of Aq/2BpAq/2 and convexity/concavity of the closely related trace functional Tr[Aq/2BpAq/2Cr]. The concavity questions are completely resolved, thereby settling cases left open by Hiai; the convexity questions are settled in many cases. As a consequence, the Audenaert-Datta Rényi entropy conjectures are proved for some cases.
Original language | English (US) |
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Pages (from-to) | 174-185 |
Number of pages | 12 |
Journal | Linear Algebra and Its Applications |
Volume | 490 |
DOIs | |
State | Published - Feb 1 2016 |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics
Keywords
- Operator concavity
- Operator convexity
- Rényi entropy
- Trace inequality