On Araki-type trace inequalities
Journal
Linear Algebra and its Applications
Journal Volume
728
Start Page
320-330
ISSN
0024-3795
Date Issued
2026-01
Author(s)
Liu, Po-Chieh
Abstract
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 ] .
Publisher
Elsevier BV
Type
journal article