有界无穷维Hamilton算子的数值半径上下界估计
Upper and Lower Bounds Estimation of Numerical Radius of Bounded Infinite-Dimensional Hamilton Operator
DOI: 10.12677/PM.2023.1311333, PDF,    科研立项经费支持
作者: 阿如汉, 耿 真, 李健龙, 田孟森, 吴德玉：内蒙古大学数学科学学院，内蒙古 呼和浩特
关键词: 数值半径；有界Hamilton算子；Hilbert空间；Numerical Radius； Bounded Hamiltonian Operator； Hilbert Space
摘要: 本文研究了有界无穷维Hamilton算子的数值半径不等式问题，利用数值半径的酉相似不变性得到了有界无穷维Hamilton算子的数值半径上下界的估计式，为刻画有界无穷维Hamilton算子谱的分布问题奠定了理论基础。
Abstract: In this paper, Numerical Radius Inequalities of bounded infinite dimensional Hamiltonian operator are studied. By applying unitary similarity invariance of numerical radius, the numerical radius upper and lower estimations of bounded infinite dimensional Hamiltonian operator are obtained, and which provides a theoretical foundation for characterizing the spectra of bounded infinite dimensional Hamiltonian operator.
文章引用：阿如汉, 耿真, 李健龙, 田孟森, 吴德玉. 有界无穷维Hamilton算子的数值半径上下界估计[J]. 理论数学, 2023, 13(11): 3204-3209. https://doi.org/10.12677/PM.2023.1311333

参考文献

[1] 钟万勰. 弹性力学求解新体系[M]. 大连: 大连理工大学出版社, 1995.
[2] Azizov, T.Ya., Dijksma, A. and Ggridneva, I.V. (2002) On the Boundness of Hamiltonian Operators. Proceedings American Mathematical Society, 131, 563-576. [Google Scholar] [CrossRef] 
[3] Kurina, G.A. (2001) Invertibility of Nonnegatively Hamiltonian Operators in a Hilbert Space. Differential Equations, 37, 880-882. [Google Scholar] [CrossRef] 
[4] Langer, H., Ran, A.C.M. and van de Rotten, B.A. (2001) Invariant Subspaces of Infinite Dimensional Hamiltonians and Solutions of the Corresponding Riccati Equations. Operator Theory: Advances and Applications, 130, 235-254. [Google Scholar] [CrossRef] 
[5] Wyss, C. (2012) Hamiltonians with Riesz Bases of General-ised Eigenvectors and Riccati Equations. Eprint Arxiv, 60, 1723-1766. [Google Scholar] [CrossRef] 
[6] 吴德玉, 阿拉坦仓, 黄俊杰, 海国君. Hilbert空间中线性算子数值域及其应用[M]. 北京: 科学出版社, 2018.

为你推荐