Criteria for monotonicity of operator means

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概要

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• Let {ψ<SUB>r</SUB>}<SUB>r>0</SUB> and {φ<SUB>r</SUB>}<SUB>r>0</SUB> be the families of operator monotone functions on [0, ∞) satisfying ψ<SUB>r</SUB>(x<SUP>r</SUP>g(x))/x<SUP>r</SUP>, φ<SUB>r</SUB>(x<SUP>r</SUP>g(x))/x<SUP>r</SUP>h(x), where g and h are continuous and g is increasing. Suppose σ_{ψ<SUB>a</SUB>} and σ_{φ<SUB>r</SUB>} are the corresponding operator connections. We will show that if A<SUP>a</SUP>σ_{ψ<SUB>a</SUB>}B≥q 1 (a>0), then A<SUP>r</SUP>σ_{ψ<SUB>r</SUB>}B and Aσ_{φ<SUB>r</SUB>}B are both increasing for r≥q a, and then we will apply this to the geometric operator means to get a simple assertion from which many operator inequalities follow.

• 社団法人 日本数学会の論文
• 2003-01-01

著者

• Uchiyama Mitsuru

  Department Of Biopharmaceutics Meiji College Of Pharmacy:division Of Drugs National Institute Of Hyg

• Uchiyama Mitsuru

  Department Of Mathematics Fukuoka University Of Education

関連論文

• POPULATION PHARMACOKINETIC APPROACH TO BIOAVAILABILITY EVALUATION FOR PHENYTOIN POWDERS
• A new majorization between functions, polynomials, and operator inequalities II
• Criteria for monotonicity of operator means

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