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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)

Abstract

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.

Keywords

Analytic Continuation Monotone Function Operator Monotone Selfadjoint Operator Dimensional Hilbert Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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