On a trace inequality

✍ Scribed by Derming Wang

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 269 KB
• Volume: 273
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(96)00520-4

✦ Synopsis

Let A andB be positive operators and p, ct, s >/0. Assume either (1) A /> B and fl >~ max{-½(p + 2a), -½(i + 2a)}, or (2) A and B are invertible with log A ~> log B and /3 >/ -a. Then, for any continuous increasing function f on •+ with f(0) = 0, the trace inequality Trf(A~(A'~BPA~)SA ~) <~ Trf(A (p+2~s+2~) holds. This generalizes both a trace inequality due to Kosaki and one due to Furuta.