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Chinese Physics B 2011年第12期20卷 264-272页

作者：齐高娃侯国林阿拉坦仓 School of Mathematical Sciences Inner Mongolia University

The completeness theorem of the eigenfunction systems for the product of two 2 × 2 symmetric operator matrices is proved. The result is applied to 4 × 4 infinite-dimensional Hamiltonian operators. A modified method of separation of variables is proposed for a separable Hamiltonian system. As an application of the theorem, the general solutions for the plate bending equation and the free vibration of rectangular thin plates are obtained. Finally, a numerical test is analysed to show the correctness of the results.

关键词： operator matrix Hamiltonian operator symplectic orthogonal eigenfunction system completeness

On the completeness of eigen and root vector systems for fourth-order operator matrices and their applications

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Chinese Physics B 2011年第10期20卷 8-14页

作者：王华阿拉坦仓黄俊杰 School of Mathematical Sciences Inner Mongolia University College of Sciences Inner Mongolia University of Technology

In this paper, we consider the eigenvalue problem of a class of fourth-order operator matrices appearing in mechan- ics, including the geometric multiplicity, algebraic index, and algebraic multiplicity of the eigenvalue, the symplectic orthogonality, and completeness of eigen and root vector systems. The obtained results are applied to the plate bending problem.

关键词： operator matrix eigenvalue problem eigenvector root vector completeness

Symplectic eigenvector expansion theorem of a class of operator matrices arising from elasticity theory

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Chinese Physics B 2011年第1期20卷 92-97页

作者：王华阿拉坦仓黄俊杰 School of Mathematical Sciences Inner Mongolia University College of Sciences Inner Mongolia University of Technology

This paper deals with the completeness of the eigenvector system of a class of operator matrices arising from elasticity theory, i.e., symplectic eigenvector expansion theorem. Under certain conditions, the symplectic orthogonality of eigenvectors of the operator matrix is demonstrated. Based on this, a necessary and sufficient condition for the completeness of the eigenvector system of the operator matrix is given. Furthermore, the obtained results are tested for the free vibration of rectangular thin plates.

关键词： operator matrix eigenvector completeness eigenvector expansion theorem

Norm Equalities and Inequalities for Three Circulant operator Matrices

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Acta Mathematica Sinica,English Series 2017年第4期33卷 571-590页

作者： Zhao Lin JIANG Yun Cheng QIAO Shu Dong WANG School of Sciences Linyi University Linyi 276005 P. R. China

In this paper, three new circulant operator matrices, scaled circulant operator matrices,diag-circulant operator matrices and retrocirculant operator matrices, are given respectively. Several norm equalities and inequalities for these operator matrices are proved. We show the special cases for norm equalities and inequalities, such as the usual operator norm and the Schatten p-norm. Pinching type inequality is also given for weakly unitarily invariant norms. These results are closely related to the nice structure of these special operator matrices. Furthermore, some special cases and specific examples are also considered.

关键词： operator matrix norm scaled circulant diag-circulant retrocirculant

The Decomposability for operator Matrices and Perturbations

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Acta Mathematica Sinica,English Series 2023年第3期39卷 497-512页

作者： Xiao Li WANG ALATANCANG School of Mathematical Sciences Inner Mongolia UniversityHohhot 010021P.R.China Statistics and Mathematics College Inner Mongolia University of Finance and EconomicsHohhot 010070P.R.China Mathematics Science College Inner Mongolia Normal UniversityHohhot 010022P.R.China

Let X and Y be Banach *** A∈L(X),B∈L(Y),C∈L(Y,X),let MCbe the operator matrix defined on X⊕Y by M_(C)=(AC0B)∈L(X⊕Y).In this paper we investigate the decomposability for *** consider Bishop’s property(β),decomposition property(δ)and Dunford’s property(C)and obtain the relationship of these properties between M_(C) and its *** explore how σ_(*)(M_(C))shrinks from σ_(*)(A)∪σ_(*)(B),where σ_(*)denotes σ_(β),σ_(δ),σ_(C),σ_(dec).In particular,we develop some sufficient conditions for equality σ_(*)(MC)=σ_(*)(A)∪σ_(*)(B).Besides,we consider the perturbation of these properties for MCand show that in perturbing with certain operators C the properties for MCkeeps with A,*** examples are given to illustrate our ***,we study the decomposability for(0AB0).Finally,we give applications of decomposability for operator matrices.

关键词： Bishop’s property(β) decomposition property(δ) Dunford’s property(C) decomposability operator matrix perturbation local spectral theory

Idempotent Completions of operator Partial Matrices

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Acta Mathematica Sinica,English Series 1999年第3期15卷 333-346页

作者： Heydar Radjavi Peter Rosenthal Department of Mathematics Shanxi Teachers University Linfen 041004 P. R. ChinaDepartment of Mathematics Statistics and Computing Science Dalhousie University Halifax N.S. B3H 3J5 Canada Department of Mathematics University of Toronto Toronto On M5S 1A1 Canada

Necessary and sufficient conditions are obtained for operator partial 2×2 matrices to have an idempotent completion, and all such completions are parametrically represented.

关键词： Hilbert space operator matrix Idempotent operator

On Principal Invariant Subspaces

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Acta Mathematica Sinica,English Series 2015年第10期31卷 1621-1628页

作者： Xiao Ming XU Xiao Chun FANG School of Science Shanghai Institute of Technology Department of Mathematics Tongji University

Let F and G be closed subspaces of the complex Hilbert spaceH, and U and V be closed subspaces of F- and G, respectively. In this paper, using the technique of operator block, we present the necessary and sufficient conditions under which （U, V） is a pair of （strictly, non-degenerate） principal invariant subspaces for （F, G）.

关键词： Hilbert space operator matrix invariant subspace principal invariant subspace

On Berezin Number Inequalities for operator Matrices

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Acta Mathematica Sinica,English Series 2021年第6期37卷 873-892页

作者： Satyajit SAHOO Namita DAS Nirmal Chandra ROUT P.G.Department of Mathematics Utkal UniversityVaniviharBhubaneswar-751004india Department of Mathematics National Institute of Techrology RaiperRaipur-492010India

In this article,we refine certain earlier existing bounds for Berezin number of operator *** also prove some new Berezin number inequalities for general n×n operator ***,we establish several upper bounds for Berezin number and generalized Euclidean Berezin number for off-diagonal operator ***,some interesting examples are discussed.

关键词： Numerical radius operator matrix Berezin number reproducing kernel

Weighted EP of Block operator Matrices

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Journal of Mathematical Research with Applications 2022年第3期42卷 230-242页

作者： Xiaopeng LI Junjie HUANG Alatancang CHEN School of Mathematical Sciences Inner Mongolia University Inner Mongolia Normal University

In this paper, we introduce and study the weighted Moore-Penrose invertible and weighted-EP of block operator matrices in the context of Hilbert spaces, based on the weighted generalized Schur complement. Furthermore,... 详细信息

关键词： EP operator weighted-EP operator operator matrix weighted generalized inverse

Quadric Completion of operator Partial Matrices (Ⅰ)

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Journal of Mathematical Research and Exposition 2000年第3期20卷 317-326页

作者：崔建莲侯晋川山西师范大学数学系临汾041004

For a given quadric polynomial p(t), the necessary and sufficient conditions are obtained for operator partial matrices of the form (~A C) to be completed to an operator T such that p(T) = 0. Moreover, all such poss... 详细信息

关键词： operator matrix completion.