Operator monotone functions induced from Löwner-Heinz inequality and strictly chaotic order

Saichi Izumino, Noboru Nakamura

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Furuta presented direct and simplified proofs of operator monotonicity of functions φ(t) = t - 1/log t and ψ(t) = t log t - t + 1/(log t) 2 by using Löwner-Heinz inequality. Extending his method, we give a sequence of operator monotone functions {fk(t)} k=0 with f0(t) = φ(t) and f 1(t) = ψ(t). We also study relations between fk(t) and strictly chaotic order defined among positive invertible operators and obtain some extensions of results due to Furuta.

Original languageEnglish
Pages (from-to)103-112
Number of pages10
JournalMathematical Inequalities and Applications
Volume7
Issue number1
DOIs
Publication statusPublished - Jan 2004
Externally publishedYes

Keywords

  • Chaotic order
  • Löwner-Heinz inequality
  • Operator monotone functions
  • Positive operators

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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