数学物理学报(英文版)

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AN ORDER PRESERVING INEQUALITY FOR THREE OPERATORS VIA FURUTA INEQUALITY

杨长森   

  1. 河南师范大学数学与信息学院, 新乡 453007
  • 收稿日期:2005-12-30 修回日期:2006-11-27 出版日期:2008-10-20 发布日期:2008-10-20
  • 通讯作者: 杨长森
  • 基金资助:

    The research was supported by Science Foundation of Ministry of Education of China (208081)

AN ORDER PRESERVING INEQUALITY FOR THREE OPERATORS VIA FURUTA INEQUALITY

Yang Changsen   

  1. College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China
  • Received:2005-12-30 Revised:2006-11-27 Online:2008-10-20 Published:2008-10-20
  • Contact: Yang Changsen

摘要:

Furuta showed that if AB ≥0, then for each r≥0, f(p)=(Ar/2BpAr/2)t+r/p+r
is decreasing for pt≥0. Using this result, the following inequality (Cr/2AB2A)δCr/2)p-1+r/4δ+rCp-1+r is obtained for 0<p≤1, r≥1, 1/4≤δ≤1 and three positive operators A, B, C satisfy (A1/2 B A1/2)p/2Ap, (B1/2 AB1/2)p/2Bp, (C1/2 AC1/2)p/2Cp, (A1/2 CA1/2)p/2Ap.

关键词: Positive operator, Furuta inequality, operator inequality

Abstract:

Furuta showed that if AB ≥0, then for each r≥0, f(p)=(Ar/2BpAr/2)t+r/p+r
is decreasing for p≥t≥0. Using this result, the following inequality (Cr/2AB2A)δCr/2)p-1+r/4δ+r≤Cp-1+r is obtained for 0<p≤1, r≥1, 1/4≤δ≤1 and three positive operators A, B, C satisfy (A1/2 B A1/2)p/2Ap, (B1/2 AB1/2)p/2Bp, (C1/2 AC1/2)p/2Cp, (A1/2 CA1/2)p/2Ap.

Key words: Positive operator, Furuta inequality, operator inequality

中图分类号: 

  • 47A63