Mathematische Annalen

, Volume 315, Issue 4, pp 771–780

Norm inequalities related to operator monotone functions

  • Tsuyoshi Ando
  • Xingzhi Zhan
Original article

DOI: 10.1007/s002080050335

Cite this article as:
Ando, T. & Zhan, X. Math Ann (1999) 315: 771. doi:10.1007/s002080050335

Abstract.

Let A,B be positive semidefinite matrices and \(|||\cdot|||\) any unitarily invariant norm on the space of matrices. We show \( |||f(A) + f(B)||| \geq |||f(A + B)|||\) for any non-negative operator monotone function f(t) on \([0,\infty)\), and \( |||g(A) + g(B)||| \leq |||g(A + B)||| \) for non-negative increasing function g(t) on \([0,\infty)\) with g(0) = 0 and \(g(\infty) = \infty\), whose inverse function is operator monotone.

Mathematics Subject Classification (1991):47A30, 47B15, 15A60

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Tsuyoshi Ando
    • 1
  • Xingzhi Zhan
    • 2
  1. 1.Faculty of Economics, Hokusei Gakuen University, Sapporo 004-8631, Japan (e-mail: ando@hokusei.ac.jp) JP
  2. 2.Institute of Mathematics, Peking University, Beijing 100871, China (e-mail: zhan@sxx0.math.pku.edu.cn) CN