### 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 {f_{k}(t)} _{k=0}
^{∞} with f_{0}(t) = φ(t) and f _{1}(t) = ψ(t). We also study relations between f_{k}(t) and strictly chaotic order defined among positive invertible operators and obtain some extensions of results due to Furuta.

Original language | English |
---|---|

Pages (from-to) | 103-112 |

Number of pages | 10 |

Journal | Mathematical Inequalities and Applications |

Volume | 7 |

Issue number | 1 |

Publication status | Published - Jan 2004 |

Externally published | Yes |

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### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Mathematical Inequalities and Applications*,

*7*(1), 103-112.

**Operator monotone functions induced from Löwner-Heinz inequality and strictly chaotic order.** / Izumino, Saichi; Nakamura, Noboru.

Research output: Contribution to journal › Article

*Mathematical Inequalities and Applications*, vol. 7, no. 1, pp. 103-112.

}

TY - JOUR

T1 - Operator monotone functions induced from Löwner-Heinz inequality and strictly chaotic order

AU - Izumino, Saichi

AU - Nakamura, Noboru

PY - 2004/1

Y1 - 2004/1

N2 - 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.

AB - 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.

KW - Chaotic order

KW - Löwner-Heinz inequality

KW - Operator monotone functions

KW - Positive operators

UR - http://www.scopus.com/inward/record.url?scp=1342305024&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1342305024&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:1342305024

VL - 7

SP - 103

EP - 112

JO - Mathematical Inequalities and Applications

JF - Mathematical Inequalities and Applications

SN - 1331-4343

IS - 1

ER -