关于算子张量积和初等算子的谱

设X,Y为复Banach空间,张量积是指关于拟一致合理范数α的完备化,B(X,Y)指从X到Y的有界线性算子全体,并设A∈B(X)~N,B∈B(Y)~M,本文给出了算子组和(L~A,R_B|B(Y,X))的联合谱和联合本质谱的表达式,进而得到了定义在上的算子及定义在B(Y,X)上初等算子的谱和本质谱的一些结果。     

复系数2n阶微分算子的谱

本文研究了复系数２ｎ阶微分算式（２．１）生成的Ｊ－自伴微分算子谱,对两类微分算子的本质谱,离散谱作了定性研究,得到了所生成微分算子本质谱的存在范围,以及所生成微分算子的谱是离散的充分条件．     

关于线性算子最小模和相似轨道的注记

本注记讨论了线性算子广义逆的稳定性和线性算子A的最小模r(A)作为B(H)上的泛函的连续性,并在此基础上指出了当算子B属于算子A的相似轨道闭包时,A和B的谱之间的联系。     

算子的左本质谱与Browder本质谱

设算子S和T拟相似,应用算子谱的精密结构的分析,证明了Browder本质谱σB(S)的连通分支与σB(T)的某些子集的相交关系以及左本质谱σle(S)的连通分支与本质谱σe(T)的某些子集的相交关系,给出左本质谱σle(S)的连通分支与σle(T)相交的充分条件和充要条件.     

算子的Kato本质谱与Browder本质谱的连通分支

利用算子谱的精密结构的分析方法,给出算子S和T拟相似时Kato本质谱σK(S)的一个连通分支与σK(T)相交的充分条件和充要条件,同时证明了Browder本质谱σB(S)的每一个连通分支与Kato本质谱σK(T)的某些子集的交集是非空的.     

一类反三角算子矩阵的本质谱

该文讨论了一类无界非自伴反三角算子矩阵的本质谱.利用二次算子族及其矩阵内部元素的性质等价刻画了算子矩阵的本质谱,并在此基础上估计了算子矩阵的本质谱的范围.最后基于本质谱的研究,讨论了其非实谱的聚点问题.     

RT类算子与右本质谱的连通分支

本文研究两个拟相似算子的右本质谱之间的相交关系.通过引进RT类算子的概念,利用算子谱的精密结构的分析方法,得到一个算子的右本质谱的连通分支与另一个拟相似算子的右本质谱相交的充分和必要条件.     

可修复人机系统的指数稳定性

研究了两相同部件温储备可修的人机系统,运用C_0半群的相关理论,对系统主算子的谱界进行估值.估算系统的算子产生的半群的增长界,然后运用了共尾的概念及相关的理论,得到了系统算子A+B的谱界与系统算子产生的半群的增长界相同.进而运用相关代数知识证得,0为系统算子的简单本征值,并分析了系统算子的谱分布,得到系统的指数稳定性.并研究了系统算子预解式的特性.对任意给定的δ0,γ=a+bi,-μ+δa_1≤a≤a_2,得到lim|b|→∞‖R(γ;A+B)‖=0.进而得到在~sRγ≥a_1的右半平面内相应于系统算子A+B的谱点由有限个本征值组成.     

板模型具广义边界条件的迁移算子的谱

研究具广义边界条件、非均匀介质、各向异性和连续能量的板模型迁移算子A的谱．证明了K=A-B的相对紧性，在L^1空间研究算子A的谱，以及占优本征值和严格占优本征值．     

二项自伴向量微分算子的本质谱

首先利用算子比较的方法,研究了二项自伴向量微分算子的本质谱,得到了这类微分算子的本质谱分布范围;然后利用算子分解定理,得到了这类算子谱的离散性的一个充分条件;最后得到了Sturm-Liouville算子和Schr?dinger算子的本质谱范围,以及这两类算子谱的离散性的一个充分条件.     

Weyl’s theorem and thin spectra

Using the notion of thin sets we prove a theorem of Weyl type for the Wolf essential spectrum ofT ∈β (H). *Further we show that Weyl’s theorem holds for a restriction convexoid operator and consequently modify some results of Berberian. Finally we show that Weyl’s theorem holds for a paranormal operator and that a polynomially compact paranormal operator is a compact perturbation of a diagnoal normal operator. A structure theorem for polynomially compact paranormal operators is also given.     

一致可逆性质及广义(ω)性质的摄动

Hilbert空间算子T∈B(H)称为是一致可逆的,若对任意的S∈B(H),TS与ST的可逆性相同.本文中根据一致可逆性质定义了一个新的谱集,用该谱集来研究广义(ω)性质的稳定性,即考虑了Hilbert空间上有界线性算子的有限秩摄动、幂零摄动以及Riesz摄动的广义(ω)性质.之后研究了能分解成有限个正规算子乘积的一类算子的广义(ω)性质的稳定性.     

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.     

Essentially subnormal operators

An operator is essentially subnormal if its image in the Calkin algebra is subnormal. We shall characterize the essentially subnormal operators as those operators with an essentially normal extension. In fact, it is shown that an essentially subnormal operator has an extension of the form ``normal plus compact'.

The essential normal spectrum is defined and is used to characterize the essential isometries. It is shown that every essentially subnormal operator may be decomposed as the direct sum of a subnormal operator and some irreducible essentially subnormal operators. An essential version of Putnam's Inequality is proven for these operators. Also, it is shown that essential normality is a similarity invariant within the class of essentially subnormal operators. The class of essentially hyponormal operators is also briefly discussed and several examples of essentially subnormal operators are given.

     

On the quasisimilarity of subnormal operators

This paper deals with the following problem: whether the quasisimilarity of subnormal operators would imply the equality of their essential spectrum. It is shown that if a subnormal operator is quasisimilar to a quasinormal operator, then they have the same essential spectrum. Furthermore, if the quasinormal operator in this case is almost normal, then they are unitarily equivalent up to a compact perturbation.     

Stability of essential spectra of singular Sturm‐Liouville differential operators under perturbations small at infinity

This paper is concerned with the stability of essential spectra of singular Sturm‐Liouville differential operators with complex‐valued coefficients. It is proved that the essential spectrum of the corresponding minimal operator is preserved by perturbations small at infinity with respect to the unperturbed operator. Based on it, 1‐dimensional Schrödinger operators under local dilative perturbations are studied.     

p-亚正常算子的本质谱与拟相似

本文证明了每一个ｐ－亚正常算子Ａ,都相应存在一个亚正常算子 ,使得Ａ与 有相同的闭值域点、相同的本质谱和谱．由此推出如果Ａ是ｐ－亚正常算子,Ｂ是任一有界线性算子,若存在有界线性算子Ｘ有稠值域,使得ＸＢ＝ＡＸ,则σ（Ａ）（Ｂ）此外还证明了,如果Ａ是ｐ－亚正常算子且 Ｒ（Ａ）闭或ＫｅｒＡ＝ＫｅｒＡ*, Ｂ是任一有界线性算子,Ａ与Ｂ拟相似,则ｅ（Ａ）（Ｂ）．     

Gustafson,weidmann, kato,wolf, schechter and browder essential spectra of some matrix operator and application to two‐group transport equation

In this paper, we investigate the Gustafson, Weidmann, Kato, Wolf, Schechter and Browder essential spectra of a 2 × 2 block matrix operator defined on a Banach space where entries are unbounded operators between Banach spaces and with domains consisting of vectors satisfying certain relations between their components under some properties. Furthermore, we give an application to two‐group transport equation. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

解析Sobolev型空间上的算子与算子代数

介绍Hardy-Sobolev空间和Fock空间及其算子与算子代数研究方面所做的工作,包括对这两类空间上几类特殊算子有界性、紧性、Fredholm性、指标理论、谱和本性谱、范数和本性范数、Schatten-p类的讨论,以及由它们所生成的C~*-代数的研究.