Lobachevskii Journal of Mathematics

, Volume 40, Issue 1, pp 101–105 | Cite as

Non-Linear Interpolation of the Harmonic–Geometric–Arithmetic Matrix Means

  • Trung Hoa DinhEmail author
  • Raluca DumitruEmail author
  • Jose A. FrancoEmail author


Bhatia, Lim, and Yamazaki conjectured that the Kubo–Ando extensions of means of numbers satisfy a norm minimality condition with respect to unitarily invariant norms. In this short note, we introduce a symmetric Kubo–Ando mean and a non-Kubo–Ando extension that do not satisfy this property.

Keywords and phrases

Kubo–Ando means symmetric means norm inequalities concavity 


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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Department of MathematicsTroy UniversityTroyUSA
  2. 2.Department of Mathematics and StatisticsUniversity of North FloridaJacksonvilleUSA

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