Extension of Löwner-Heinz Inequality Via Analytic Continuation

  • Mitsuru Uchiyama
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 9)


That t α (0 < α < 1) is operator monotone on [0, ∞) means, by definition, 0 ≤ ABA α B α , which is called a Löwner-Heinz inequality. We consider the converse of this statement. We systematically construct a family of operator monotone functions which includes t α . Moreover, we give operator inqualities which are extensions of those by Furuta and Ando.


Analytic Continuation Monotone Function Operator Monotone Selfadjoint Operator Dimensional Hilbert Space 
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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Mitsuru Uchiyama
    • 1
  1. 1.Department of MathematicsFukuoka University of EducationMunakata,FukuokaJapan

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