On Araki-type trace inequalities
In this paper, we prove a trace inequality Tr [ f ( A ) A s B s ] ≤ Tr [ f ( A ) ( A 1 / 2 B A 1 / 2 ) s ] for any positive and monotonically increasing function f , s ∈ [ 0 , 1 ] , and positive semi-definite matrices A and B . On the other hand, if s ∈ [ 0 , 1 ] and the map x ↦ x s g ( x ) is positive and decreasing, then Tr [ g ( A ) ( A 1 / 2 B A 1 / 2 ) s ] ≤ Tr [ g ( A ) A s B s ] .
Authors
- Po-Chieh Liu
- Hao–Chung Cheng (ORCID: https://orcid.org/0000-0003-4499-4679)
Institutions
- National Taiwan University of Science and Technology (TW)
- National Taiwan University (TW)
- Foxconn (Taiwan) (TW)
- National Center for Theoretical Sciences (TW)
Publication Details
- Journal
- Linear Algebra and its Applications
- Published
- 2025-09-04
- DOI
- https://doi.org/10.1016/j.laa.2025.08.023
- Citations
- 1
- Primary Topic
- Mathematical Inequalities and Applications
- Type
- article
- Field-Weighted Citation Impact
- 3.73