| 关于三个算子的算子不等式(英文) |
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| 引用本文： | 杨长森,王亚青. 关于三个算子的算子不等式(英文)[J]. 数学季刊, 2011, 0(3): 335-342 |
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| 作者姓名： | 杨长森 王亚青 |
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| 作者单位： | College of Mathematics and Information Science;Henan Normal University; |
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| 基金项目： | Supported by the Science Foundation of Ministry of Education of China(208081); Supported by the Natural Science Foundation of Henan Province(102300410012,2007110016,2008B110006) |
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| 摘 要： | As a generalization of grand Furuta inequality,recently Furuta obtain：If A≥ B≥0 with A0,then for t∈[0,1]and p1,p2,p3,p4≥1, A t 2[A- t 2{A t 2（A/ t 2 Bp 1A /t2 ）p 2A t 2}p 3A -t2 ]p 4A t 2 1 [{（p1/t）p2＋t}p3-t]p4＋t]≤A. In this paper,we generalize this result for three operators as follow：If A≥B≥C≥0 with B0,t∈[0,1]and p1,p2,···,p2n/1,p2n≥1 for a natural number n.Then the following inequalities hold for r≥t, A1/t＋r≥ [A r 2[B /t 2{B t 2······[B /t 2{B t 2（B /t 2 ←B /t 2 n times Bt 2 n/1 times by turns Cp 1B /t 2）p 2B t 2}p 3B /t 2]p 4···B t 2}p 2n/1B /t 2 B /t 2 n times Bt 2 n/1 times by turns→ ]p 2nA r 2] 1/t＋r q[2n]＋r/t, where q[2n]≡{···[{[（p1-t）p2＋t]p3/t}p4＋t]p5/···/t}p2n＋t /t and t alternately n times appear .
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| 关 键 词： | Furuta inequality grand Furuta inequality order preserving operator inequality |
An Operator Inequality for Three Operators |
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| YANG Chang-sen,WANG Ya-qing. An Operator Inequality for Three Operators[J]. Chinese Quarterly Journal of Mathematics, 2011, 0(3): 335-342 |
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| Authors: | YANG Chang-sen WANG Ya-qing |
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| Affiliation: | YANG Chang-sen,WANG Ya-qing (College of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,China) |
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| Abstract: | |
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| Keywords: | Furuta inequality grand Furuta inequality order preserving operator inequality |
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