摘要
本文主要研究了无穷维复Hilbert空间中有界分块算子矩阵的数值半径问题.首先研究了斜对角分块算子矩阵数值半径不等式的推广形式,并利用数值半径的酉相似不变性和广义混合Schwarz不等式给出了两个有界线性算子和的数值半径的不等式;其次给出了2×2有界分块算子矩阵的数值半径不等式;最后将结论应用到有界无穷维Hamilton算子,描述出其数值半径的不等式.
In this paper,the numerical radius of bounded block operator matrices on Hilbert space is studied.First,the generalized form of numerical radius inequalities of off-diagonal block operator matrix is studied,and taking advantage of the unitary similarity invariance of numerical radius and the generalized mixed Schwarz inequality,the inequalities of the numerical radius of sum of two bounded linear operators are considered.Then,numerical radius inequalities for 2×2 bounded block operator matrices are given.Finally,the conclusion is applied in the bounded infinite dimensional Hamiltonian operator and the inequalities of its numerical radius are obtained.
作者
邬慧婷
吴德玉
阿拉坦仓
Hui Ting WU;De Yu WU;Alatancang(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,P.R.China;Hohhot Minzu College,Hohhot 010050,P.R.China)
出处
《数学学报（中文版）》
CSCD
北大核心
2021年第3期375-384,共10页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金资助项目(11561048,11761029)
内蒙古自然科学基金资助项目(2019MS01019)。
关键词
数值域
数值半径
分块算子矩阵
无穷维HAMILTON算子
numerical range
numerical radius
block operator matrices
infinite dimensional Hamiltonian operator
