关于三个算子的算子不等式

数学季刊 ›› 2011, Vol. 26 ›› Issue (3): 335-342.

关于三个算子的算子不等式

College of Mathematics and Information Science, Henan Normal University

收稿日期:2009-09-15 出版日期:2011-09-30 发布日期:2023-04-18
作者简介:YANG Chang-sen(1965-), male, native of Xinxiang, Henan, a professor of Henan Normal University, Ph.D., engages in functional analysis; WANG Ya-qing(1983-), female, native of Puyang, Henan, a master student of Henan Normal University, engages in functional analysis.
基金资助:
Supported by the Science Foundation of Ministry of Education of China(208081)； Supported by the Natural Science Foundation of Henan Province(102300410012,2007110016,2008B110006)；

An Operator Inequality for Three Operators

College of Mathematics and Information Science, Henan Normal University

Received:2009-09-15 Online:2011-09-30 Published:2023-04-18
About author:YANG Chang-sen(1965-), male, native of Xinxiang, Henan, a professor of Henan Normal University, Ph.D., engages in functional analysis; WANG Ya-qing(1983-), female, native of Puyang, Henan, a master student of Henan Normal University, engages in functional analysis.
Supported by:
Supported by the Science Foundation of Ministry of Education of China(208081)； Supported by the Natural Science Foundation of Henan Province(102300410012,2007110016,2008B110006)；

摘要/Abstract

摘要： As a generalization of grand Furuta inequality, recently Furuta obtain: If A≥ B≥0 with A>0, then for t∈[0,1] and p₁, p₂, p₃, p₄≥1, .... In this paper, we generalize this result for three operators as follow: If A≥B≥C≥0 with B>0, t∈[0,1] and p₁, p₂, ···, p_2n-1, p_2n≥1 for a natural number n. Then the following inequalities hold for r≥t, ..., where q_[2n]≡···.

关键词: Furuta inequality, grand Furuta inequality, order preserving operator inequality

Abstract: As a generalization of grand Furuta inequality, recently Furuta obtain: If A≥ B≥0 with A>0, then for t∈[0,1] and p₁, p₂, p₃, p₄≥1, .... In this paper, we generalize this result for three operators as follow: If A≥B≥C≥0 with B>0, t∈[0,1] and p₁, p₂, ···, p_2n-1, p_2n≥1 for a natural number n. Then the following inequalities hold for r≥t, ..., where q_[2n]≡···.

Key words: Furuta inequality, grand Furuta inequality, order preserving operator inequality

中图分类号:

O177

杨长森, 王亚青 . 关于三个算子的算子不等式[J]. 数学季刊, 2011, 26(3): 335-342.

YANG Chang-sen, WANG Ya-qing. An Operator Inequality for Three Operators[J]. Chinese Quarterly Journal of Mathematics, 2011, 26(3): 335-342.

[1]	代辉亚, 杨长森. 有关p-亚正规算子和对数亚正规算子广义Aluthge变换的一个注解[J]. 数学季刊, 2008, 23(4): 525-532.
[2]	高福根, 杨长森. 关于logA≥logB的一个注记[J]. 数学季刊, 2008, 23(1): 135-139.
[3]	杨长森, 李海英. p-ω-亚正规算子[J]. 数学季刊, 2005, 20(1): 79-84.