An inequality for expectation of means of positive random variables

Paolo Gibilisco, Frank Hansen

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Suppose that X, Y are positive random variables and m is a numerical (commutative) mean. We prove that the inequality E(m(X, Y)) ≤ m(E(X), E(Y)) holds if and only if the mean is generated by a concave function. With due changes we also prove that the same inequality holds for all operator means in the Kubo{Ando setting. The case of the harmonic mean was proved by C. R. Rao and B. L. S. Prakasa Rao.

Original languageEnglish
Pages (from-to)142-151
Number of pages10
JournalAnnals of Functional Analysis
Issue number1
Publication statusPublished - 2017


  • Concavity
  • Numerical means
  • Operator means
  • Random matrices

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory


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