Reverse inequality to Golden–Thompson type inequalities: Comparison of and

✍ Scribed by Jean-Christophe Bourin; Yuki Seo

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 111 KB
• Volume: 426
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2007.05.002

✦ Synopsis

Let A and B be n-by-n Hermitian matrices. Then Tr e A e B S(α)Tr e A+B

where α is the condition number of e A and S(t) is the Specht ratio of the reverse arithmetic-geometric mean inequality. It is a sharp reverse result to the Golden-Thompson inequality. This can be extended to each eigenvalue. Equivalently there exists a unitary V such that e A/2 e B e A/2 S(α)V e A+B V * .

We also show that there exists a unitary W such that W e A+B W * S(α)e A/2 e B e A/2 .