Generalized noncommutative Hardy and Hardy-Hilbert type inequalities

Frank Hansen, Kristina Krulić, Josip Pečarić, Lars Erik Persson

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We extend and unify several Hardy type inequalities to functions whose values are positive semi-definite operators. In particular, our methods lead to the operator versions of Hardy-Hilbert's and Godunova's inequalities. While classical Hardy type inequalities hold for parameter values p > 1, it is typical that the operator versions hold only for 1 < p ≤ 2, even for functions with values in 2 × 2 matrices.

Original languageEnglish
Pages (from-to)1283-1295
Number of pages13
JournalInternational Journal of Mathematics
Volume21
Issue number10
DOIs
Publication statusPublished - 2010 Oct 1

Keywords

  • Godunova's inequality
  • Hardy's inequality
  • Hardy-Hilbert's inequality
  • Inequalities
  • operator convex functions
  • positive operator
  • weights

ASJC Scopus subject areas

  • Mathematics(all)

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