2×2分块对角算子矩阵拟谱的精细刻画

设A,B为可分Hilbert空间X中的稠定闭线性算子,■表示2×2分块算子矩阵.文中精细刻画算子矩阵M₀在对角扰动情形下的拟点谱、拟剩余谱与拟连续谱,所得结论与点谱、剩余谱和连续谱的结果进行了比较,并用例子进行了辅证.最后,采用空间分解技巧,用主对角元的信息刻画M₀在上三角扰动情形下的拟点谱分布.     

一类无界算子的点谱,连续谱,剩余谱间的关系

证明了在Ｈｉｌｂｅｒｔ空间中拟相似的闭稠定线性算子有相同的点谱、剩余谱、对于拟相似的闭形式亚正规算子还有相同的连续谱。     

上三角闭算子矩阵的本质谱和Weyl谱性质

本文主要研究了上三角闭算子矩阵TB=(AB0D):D(A)(+) D(D)(∪)H(+)K→H(+)K的本质谱和Weyl谱的性质,其中H和K都是无穷维复可分的Hilbert空间.首先,对给定的稠定闭算子A和D,得到了存在可闭算子B使得TB是半Weyl和半Fredholm算子的充分必要条件,其中B满足D(B)(∩)D(D...     

上三角无穷维Hamilton算子的剩余谱

将点谱划分为四个部分,得到上三角无穷维Hamilton算子的点谱σ_p(H)关于虚轴对称的充要条件.在此基础上,结合无穷维Hamilton算子的谱结构,得到无穷维Hamilton算子剩余谱的完全描述,从而实现了利用其内部算子刻画剩余谱.     

L^2*L^2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L^2*L^2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.     

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．     

无穷维Hamilton算子的谱结构

研究无穷维Hamilton算子的谱结构. 得到无穷维Hamilton算子的谱、点谱和剩余谱之并集和连续谱均关于虚轴对称. 此外, 还证明了无穷维Hamilton算子的剩余谱不含有任何关于虚轴对称的点对, 从而利用点谱完全刻画了剩余谱. 作为谱结构的应用, 得到一类无穷维Hamilton算子剩余谱为空集的若干充分必要条件.     

带有反馈与起动故障的M/G/1重新访问排队系统的适定性分析

文章研究一个带有贝努利反馈且系统服务台经常遭受启动故障的重新访问排队系统模型,利用线性算子半群理论,通过对描述其系统行为的偏微分方程组的研究,证明了该模型所描述的系统所确定的算子是闭稠定耗散算子,生成C0压缩半群,从而得到系统的适定性.在证明1是算子的预解点时,采用了共轭方法.     

缺项3×3上三角算子矩阵的可能谱

根据值域的稠密性和闭性,可将有界线性算子的点谱和剩余谱进一步细分为1,2-类点谱和1,2-类剩余谱.针对3×3阶上三角算子矩阵,采用分析方法和空间分解方法分别刻画了可能1,2-类点谱和可能1,2-类剩余谱.     

Banach空间中线性算子的(集值)度量广义逆的表示及应用

在Banach空间Y无自反和从Banach空间X到Y的线性算子T无闭值域和稠定的假定下,利用Banach空间几何方法证明了Banach空间中线性算子的度量广义逆是具有闭凸值的集值映射,建立了该度量广义逆的存在性、唯一性和等价表达式,并给出了此表达式的一个应用示例．所得的部分结果本质地拓广王玉文和潘少荣在Banach空间Y自反,从X到Y的线性算子T为闭值域和稠定的假定下的近期相应结果．     

Perturbation of semi-Browder operators and stability of Browder's essential defect and approximate point spectrum

In the present paper we investigate the stability of closed densely defined semi-Browder operators under operator perturbations that belong to a perturbation class related to compact operators. Furthermore, we apply the obtained results to give a characterization and to study the stability of Browder's essential approximate point spectrum and Browder's essential defect spectrum.     

BROWDER AND SEMI-BROWDER OPERATORS＊

In this article,we study characterization,stability,and spectral mapping theorem for Browder's essential spectrum,Browder's essential defect spectrum and Browder's essential approximate point spectrum ...     

Characterization of Closed Densely Defined Semi-Browder Linear Operators

In the present paper we characterize the closed densely defined semi-Browder operators through the Kato decomposition. Furthermore, we apply the obtained results to give a new characterization of Browder’s essential defect spectrum and Browder’s essential approximate point spectrum under finite rank operator perturbations.     

Relative essential spectra involving relative demicompact unbounded linear operators

In this article, we introduce the concept of demicompactness with respect to a closed densely defined linear operator, as a generalization of the class of demicompact operator introduced by Petryshyn in [24] and we establish some new results in Fredholm theory. Moreover, we apply the obtained results to discuss the incidence of some perturbation results on the behavior of relative essential spectra of unbounded linear operators acting on Banach spaces. We conclude by characterizations of the relative Schechter's and approximate essential spectrum.     

A characterization of some subsets of Schechter's essential spectrum and application to singular transport equation

The purpose of this paper is to provide a detailed treatment of some subsets of Schechter's essential spectrum of closed, densely defined linear operators subjected to additive perturbations. Our results are used to describe the essential approximate point spectrum and the essential defect spectrum of singular neutron transport operators in bounded geometries.     

RELATIVE ESSENTIAL SPECTRA INVOLVING RELATIVE DEMICOMPACT UNBOUNDED LINEAR OPERATORS

In this article, we introduce the concept of demicompactness with respect to a closed densely defined linear operator, as a generalization of the class of demicompact operator introduced by Petryshyn in [24] and we establish some new results in Fredholm theory. Moreover, we apply the obtained results to discuss the incidence of some perturbation results on the behavior of relative essential spectra of unbounded linear operators acting on Banach spaces. We conclude by characterizations of the relative Schechter＇s and approximate essential spectrum.