二次数值半径相关问题研究
Research on the Related Problems of Quadratic Numerical Radius
DOI: 10.12677/AAM.2019.84095, PDF,    科研立项经费支持
作者: 刘佳伟, 孙自杰, 赵锦芳, 胡宝月, 鲍聪慧, 吴德玉:内蒙古大学数学科学学院,内蒙古 呼和浩特
关键词: 二次数值半径幂不等式数值半径Quadratic Numerical Radius Power Inequality Numerical Radius
摘要: 本文利用Spectraloid算子及分块算子矩阵的方法研究了有界分块算子矩阵的二次数值半径不等式的问题,得到两个乘积算子的二次数值半径不等式及分块算子矩阵的二次数值半径幂不等式的性质。
Abstract: In this paper, the quadratic numerical radius of 2 × 2 block operator matrices is studied by method of Spectraloid operator and block operator matrices, and the multiplicative properties of quadratic numerical radius and power inequality of quadratic numerical radius are obtained.
文章引用:刘佳伟, 孙自杰, 赵锦芳, 胡宝月, 鲍聪慧, 吴德玉. 二次数值半径相关问题研究[J]. 应用数学进展, 2019, 8(4): 852-857. https://doi.org/10.12677/AAM.2019.84095

参考文献

[1] 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.
[2] Markus, A., Matsaev, V. and Tretter, C. (2001) A New Concept for Block Operator Matrices: The Quadratic Numerical Range. Linear Algebra and Its Applications, 330, 89-112. [Google Scholar] [CrossRef
[3] Tretter, C. (2008) Spectral Theory of Block Operator Ma-trices and Applications. Imperial College Press, Covent Garden, London, UK. [Google Scholar] [CrossRef
[4] Raodkm, G.K. (1997) Numerical Range. Springer-Verlag, New York. [Google Scholar] [CrossRef
[5] Sinclair, A.M. (1970) Eigenvalues in the Boundary of the Nu-merical Range. Pacific Journal of Mathematics, 35, 231-234. [Google Scholar] [CrossRef
[6] Deyu, W. and Atatancang, C. (2011) Invertibility of Nonnegative Hamiltonian Operator with Unbounded Entries. rossref.org/SimpleTextQuery, 373, 410-413. [Google Scholar] [CrossRef
[7] Deyu, W. and Ata-tancang, C. (2011) Spectral Inclusion Properties of the Numerical Range in a Space with an Indefinite Metric. Linear Algebra and Its Applications, 435, 1131-1136. [Google Scholar] [CrossRef
[8] 吴德玉, 阿拉坦仓. 分块算子矩阵谱理论及其应用[M]. 北京: 科学出版社, 2013.