Complementary Inequalities to Improved AM-GM Inequality

Following an idea of Lin, we prove that if A and B are two positive operators such that 0 〈 mI 〈 A 〈 m＇I ≤ M＇I ≤B 〈 MI, then Ф^2（A＋B/2）≤K^2（h）/（1＋（logM＇/m＇）^2/8）^2Ф^2（A#B）,and Ф^2（A＋B/2）≤K^2（h）/（1＋（logM＇/m＇）^2/8）^2（Ф（A）#Ф（B））^2,where K（h） = （h＋1）2 /4h and h = M and Ф is a positive unital linear map....

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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2017-12, Vol.33 (12), p.1609-1616
Main Authors: Moradi, Hamid Reza, Omidvar, Mohsen Erfanian
Format: Article
Language:English
Subjects:
Mathematical analysis
Mathematics
Mathematics and Statistics
互补
单位元
均值不等式
正算子
线性映射
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Summary:Following an idea of Lin, we prove that if A and B are two positive operators such that 0 〈 mI 〈 A 〈 m＇I ≤ M＇I ≤B 〈 MI, then Ф^2（A＋B/2）≤K^2（h）/（1＋（logM＇/m＇）^2/8）^2Ф^2（A#B）,and Ф^2（A＋B/2）≤K^2（h）/（1＋（logM＇/m＇）^2/8）^2（Ф（A）#Ф（B））^2,where K（h） = （h＋1）2 /4h and h = M and Ф is a positive unital linear map.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-017-7118-y