A\(\geq B\geq 0\) iff \((B^ rA^ pB^ r)^{1/q}\geq B^{(p+2r)/q}\) for r\(\geq 0\), p\(\geq 0\), q\(\geq 1\) with \((1+2r)q\geq p+2r\)

DOI10.3792/pjaa.63.4zbMath0619.47021OpenAlexW2035958560MaRDI QIDQ1089602

Takayuki Furuta

Publication date: 1987

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.63.4

zbMATH Keywords

operator monotone functionpositive operatororder preserving operator inequalities

Mathematics Subject Classification ID

Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15)

Cites Work

• Über monotone Matrixfunktionen
• Some inequalities for the rational power of a nonnegative definite matrix
• Beiträge zur Störungstheorie der Spektralzerlegung
• Notes on some inequalities for linear operators
• Hermitian Matrix Inequalities and a Conjecture
• Inequalities for the Powers of Nonnegative Hermitian Operators
• Shorter Notes: Some Operator Monotone Functions
• Shorter Notes: The Operator Equation THT = K
• An operator inequality

This page was built for publication: A\(\geq B\geq 0\) iff \((B^ rA^ pB^ r)^{1/q}\geq B^{(p+2r)/q}\) for r\(\geq 0\), p\(\geq 0\), q\(\geq 1\) with \((1+2r)q\geq p+2r\)