Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.05242 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908556298551296 |
|---|---|
| author | Liu, Po-Chieh Cheng, Hao-Chung |
| author_facet | Liu, Po-Chieh Cheng, Hao-Chung |
| contents | In this paper, we prove a trace inequality $\text{Tr}[ f(A) A^s B^s ] \leq \text{Tr}[ f(A) (A^{1/2} B A^{1/2} )^s ]$ for any positive and monotone increasing function $f$, $s\in[0,1]$, and positive semi-definite matrices $A$ and $B$. On the other hand, for $s\in[0,1]$ such that the map $x\mapsto x^s g(x)$ is positive and decreasing, then $ \text{Tr}[ g(A) (A^{1/2} B A^{1/2} )^s ] \leq \text{Tr}[ g(A) A^s B^s ]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05242 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Araki-Type Trace Inequalities Liu, Po-Chieh Cheng, Hao-Chung Mathematical Physics Functional Analysis Quantum Physics Primary 15A42, 15A45, 15A60, 47A60 In this paper, we prove a trace inequality $\text{Tr}[ f(A) A^s B^s ] \leq \text{Tr}[ f(A) (A^{1/2} B A^{1/2} )^s ]$ for any positive and monotone increasing function $f$, $s\in[0,1]$, and positive semi-definite matrices $A$ and $B$. On the other hand, for $s\in[0,1]$ such that the map $x\mapsto x^s g(x)$ is positive and decreasing, then $ \text{Tr}[ g(A) (A^{1/2} B A^{1/2} )^s ] \leq \text{Tr}[ g(A) A^s B^s ]$. |
| title | On Araki-Type Trace Inequalities |
| topic | Mathematical Physics Functional Analysis Quantum Physics Primary 15A42, 15A45, 15A60, 47A60 |
| url | https://arxiv.org/abs/2507.05242 |