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

Saichi Izumino; Noboru Nakamura

doi:10.7153/mia-07-12

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

Saichi Izumino, Noboru Nakamura

Research output: Contribution to journal › Article › peer-review

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 {f_k(t)} _k=0^∞ with f₀(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
DOIs	https://doi.org/10.7153/mia-07-12
Publication status	Published - Jan 2004
Externally published	Yes

Keywords

Chaotic order
Löwner-Heinz inequality
Operator monotone functions
Positive operators

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.7153/mia-07-12

Cite this

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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 L{\"o}wner-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.",

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AU - Nakamura, Noboru

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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

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DO - 10.7153/mia-07-12

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AN - SCOPUS:1342305024

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JO - Mathematical Inequalities and Applications

JF - Mathematical Inequalities and Applications

IS - 1

ER -

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

Abstract

Keywords

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