n × n 上三角算子矩阵的单值扩张性以及应用*

设X_i是无穷维复Banach空间, L(X_j,X_i)是X_j到X_i上的有界线性算子全体.考虑 n × n 上三角算子矩阵T=(T_ij)_1≤j≤n, 其中T_ij L(X_j,X_i),1≤j≤n; T_ij=0, i>j.本文研究了T的单值扩张性, 通过考察集合S(T)={λ∈C}: T在点λ没有SVEP},证明了S(T)在i=1 ? nS(T_i)中退化,进而给出等式S(T)=i=1 ? n S(T_i)成立的条件. 同时, 考察了T的单值扩张性扰动,得到了S(T)保持对角稳定时T_i所需的条件并予以证明, 同时举例说明这些条件的合理性.最后, 给出单值扩张性关于谱σ(T)和局部谱σT (x)的应用, 得到了谱扰动和局部谱扰动不变的新条件.     

THE HAMILTONIAN SYSTEM AND COMPLETENESS OF SYMPLECTIC ORTHOGONAL SYSTEM

I.IntroductionThemethodofseparationofvariablesisimportanttosolvethesoluti0n0fprobIem0fmathematicalphysics,butmanyproblen1sofmathematicalphysicscannotseparatet'ariab1es,thereforeitrestrictstheranget0appIicatemethodofseparationofvariable.Inthepaperlll,Zhong…     

Symplectic Self-adjointness of Infinite Dimensional Hamiltonian Operators

Symplectic self-adjointness of infinite dimensional Hamiltonian operators is studied, the necessary and sufficient conditions are given. Using the relatively bounded perturbation, the sufficient conditions about symplectic self-adjointness are shown.     

无界奇异∮-自伴算子矩阵的可逆性与可逆补

刻画了2×2无界奇异∮-自伴算子矩阵的可逆性,并且得到相应的缺项算子矩阵存在可逆补的充分必要条件,最后举例验证了结果的合理性.     

非负Hamilton算子的可逆性

研究了非负Hamilton算子H=(ACB-A*)的可逆性以及有界逆的存在性问题,进而给出了非负Hamilton算子H存在有界逆以及虚轴上的点均为H的正则点的充分条件.     

上三角无穷维Hamilton算子点谱的对称性

In this paper, by using characterization of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator H, a necessary and sufficient condition is obtained on the symmetry of σP（A） and σ1/P（-A^＊） with respect to the imaginary axis. Then the symmetry of the point spectrum of H is given, and several examples are presented to illustrate the results.     

无穷维Hamilton算子的二次数值域

研究了一类无界无穷维Hamilton算子的二次数值域的性质,进而,应用二次数值域来刻画了无穷维Hamilton算子谱的分布范围,并给出了二次数值域的闭包包含谱集的结论.     

Possible Spectrums of 3×3 Upper Triangular Operator Matrices

Let H1, H2 and H3 be infinite dimensional separable complex Hilbert spaces. We denote by M(D,E,F) a 3×3 upper triangular operator matrix acting on H1⊕H2⊕H3 of the form M(D,E,F)=(A D E 0 B F 0 0 C). For given A ∈ B(H1), B ∈ B(H2) and C ∈ B(H3), the sets UD,E,F σp(M(D,E,F)), ∪D,E,F σr(M(D,E,F)), ∪D,E,F σc(M(D,E,F)) and ∪D,E,F σ(M(D,E,F)) are characterized, where D ∈ B(H2,H1), E ∈ B(H3, H1), F ∈ B(H3, H2) and σ(·), σp(·), σr(·),σc(·) denote the spectrum, the point spectrum, the residual spectrum and the continuous spectrum, respectively.     

L2×L2中的一类无穷维Hamilton算子的剩余谱

该文得到了一类无穷维Hamilton算子的剩余谱和点谱存在的几个判别准则,从而给出 了求其剩余谱和点谱的方法．在此基础上构造了L2×L2中无穷维Hamilton算子的剩余谱 非空的具体例子,从而进一步验证了判别准则的有效性．