PDF(417 KB)
PDF(417 KB)
PDF(417 KB)
有界分块算子矩阵的数值半径估计
Numerical Range Estimation of Block Operator Matrices
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.
数值域 / 数值半径 / 分块算子矩阵 / 无穷维Hamilton算子 {{custom_keyword}} /
numerical range / numerical radius / block operator matrices / infinite dimensional Hamiltonian operator {{custom_keyword}} /
[1] Abu-Omar A., Kittaneh F., Numerical radius inequalities for n×n operator matrices, Linear Algebra and Its Appl., 2015, 468(1):18-26.
[2] Ando T., Aluthge transforms and the convex hull of the eigenvalues of a matrix, Linear and Multilinear Algebra, 2002, 52(3):281-292.
[3] Azizov T. Y., Dijksma A., Gridneva I., On the boundedness of Hamiltonian operators, P. Am. Math. Soc., 2003, 131(2):563-576.
[4] Bani-Domi W., Kittaneh F., Norm equalities and inequalities for operator matrices, Linear Algebra Appl., 2008, 429(1):57-67.
[5] Bani-Domi W., Kittaneh F., Numerical radius inequalities for operator matrices, Linear and Multilinear Algebra, 2009, 57(4):421-427.
[6] Goldberg M., Tandmor E., On the numerical radius and its applications, Linear Algebra and Its Appl., 1982, 42:263-284.
[7] Hirzallah O., Kittench F., Shebrawi K., Numerical radius inequalities for commutators of Hilbert space operators, Numer. Func. Anal. Opt., 2011, 32(7):739-749.
[8] Hirzallah O., Kittaneh F., Shebrawi K., Numerical radius inequalities for certain 2×2 operator matrices, Integr. Equ. Oper. Theory, 2011, 71(1):129-147.
[9] Kittaneh F., Notes on some inequalities for Hilbert space operators, Publ. Res. Ins. Math. Sci., 1988, 24(1):283-293.
[10] Kittaneh F., Norm inequalities for certain operator sums, Journal of Funct. Anal., 1997, 143(2):337-348.
[11] Kittaneh F., A numerical radius inequalities and an estimate for numerical radius of the Frobenius companion matrix, Studia Math., 2003, 158(1):11-17.
[12] Kittaneh F., Norm inequalities for sums and differences of positive operators, Linear Algebra Appl., 2004, 383(1):85-91.
[13] Kittaneh F., Numerical radius inequalities for Hilbert space operators, Studia Math., 2005, 168(1):73-80.
[14] Li C. K., Tam T. Y., Tsing N. K., The generalized spectral radius, numerical radius and spectral norm, Linear and Multilinear Algebra, 1984, 16(1):215-237.
[15] Pearcy C., An elementary proof of the power inequality for the numerical radius, Michigan Math. J., 1966, 13(3):289-291.
[16] Sun J., Wang Z., Spectral Analysis of Linear Operators (in Chinese), Science Press, Beijing, 2005.
[17] Wu D. Y., Chen A., Spectral Theory of Block Operator Matrices and Applications (in Chinese), Science Press, Beijing, 2013.
[18] Wu D. Y., Chen A., Huang J. J., et al., Numerical Range of Linear Operators on Hilbert Space and Its Applications (in Chinese), Science Press, Beijing, 2018.
[19] Yamazaki T., On upper and lower bounds of the numerical radius and an equality condition, Studia Math., 2007, 178(1):83-89.
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）
/
| 〈 |
|
〉 |
