半-Hilbert空间中的几类数值半径不等式  

Some Numerical Radius Inequalities in Semi-Hilbert Space

作　　者：赵佳佳 乔宏伟 海国君[1] ZHAO Jiajia;QIAO Hongwei;HAI Guojun(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China;School of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China)

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021 [2]内蒙古师范大学数学科学学院,呼和浩特010022

出　　处：《内蒙古大学学报（自然科学版）》2024年第6期403-411,共9页Journal of Inner Mongolia University：Natural Science Edition

基　　金：内蒙古自然科学基金项目(2020ZD01);内蒙古一流学科科研专项(YLXKZX-NSD-017)。

摘　　要：研究了由正算子A诱导的半内积〈·,·〉_(A)生成的半-Hilbert空间中的数值半径不等式。利用幂平均不等式等改进了已有的半-Hilbert空间中的数值半径的上界与下界,并与已有的不等式进行了比较,在最后的结论中也得到了等号成立的条件。The numerical radius was studied in semi-Hilbert space with the semi-product 〈·,·〉_(A) induced by the positive operator A.The upper and lower bound of numerical radius in semi-Hilbert space was improved by using basic inequalities,such as the power mean inequality.And the comparision with the existing inequalities was given.We also obtained a condition for establishing the equality sign in the final conclusion.

关 键 词：A-数值半径 不等式 正算子 半-Hilbert空间 

分 类 号：O178[理学—数学] O177.1[理学—基础数学]