Integral Equations and Operator Theory

, Volume 42, Issue 2, pp 243–251

On some operator monotone functions

  • Mitsuru Uchiyama
  • Morisuke Hasumi

DOI: 10.1007/BF01275518

Cite this article as:
Uchiyama, M. & Hasumi, M. Integr equ oper theory (2002) 42: 243. doi:10.1007/BF01275518


We try to find a continuous functionu defined on a real right half-line with the range (0, ∞) such thatu−1 is operator monotone. We then look for another functionv such thatv(u−1) is operator monotone, namely,u(A)≦u(B) impliesv(A)≦v(B) for self-adjoint operatorsA andB.

Subject Classification

Primary 15A39 47A63 Secondary 30B40 

Copyright information

© Birkhäuser Verlag 2002

Authors and Affiliations

  • Mitsuru Uchiyama
    • 1
  • Morisuke Hasumi
    • 2
  1. 1.Department of MathematicsFukuoka University of EducationMunakata, FukuokaJapan
  2. 2.Department of Mathematical SciencesIbaraki UniversityMito, IbarakiJapan

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