Wely定理与$(\omega)$性质的等价性

We call T C B（H） consistent in Fredholm and index （briefly a CFI operator） if for each B ∈ B（H）, TB and BT are Fredholm together and the same index of B, or not Fredholm together. Using a new spectrum defined in view of the CFI operator, we give the equivalence of Weyl＇s theorem and property （ω） for T and its conjugate operator T^＊. In addition, the property （ω） for operator matrices is considered.     

Property (ω) and Its Perturbations

In the note,we establish for a bounded linear operator defined on a Hilbert space the necessary and sufficient conditions for the stability of property(ω) by means of the variant of the essential approximate point spectrum and the induced spectrum of consistency in Fredholm and index.In addition,the stability of property(ω) for H(P) operators is considered.     

$(\omega)$性质及其摄动

In the note,we establish for a bounded linear operator defined on a Hilbert space the necessary and sufficient conditions for the stability of property(ω) by means of the variant of the essential approximate point spectrum and the induced spectrum of consistency in Fredholm and index.In addition,the stability of property(ω) for H(P) operators is considered.     

Property (ω′) and Its Perturbation

In this note we define the property (ω′), a variant of Weyl’s theorem, and establish for a bounded linear operator defined on a Hilbert space the necessary and sufficient conditions for which property (ω′) holds by means of the variant of the essential approximate point spectrum σ1(·) and the spectrum defined in view of the property of consistency in Fredholm and index. In addition, the perturbation of property (ω′) is discussed.     

$(\omega'')$性质及其摄动

In this note we define the property （ω′）, a variant of Weyl’s theorem, and establish for a bounded linear operator defined on a Hilbert space the necessary and sufficient conditions for which property （ω′） holds by means of the variant of the essential approximate point spectrum σ1（·） and the spectrum defined in view of the property of consistency in Fredholm and index. In addition, the perturbation of property （ω′） is discussed.     

Property(ω) and Its Perturbations

A Hilbert space operator T is said to have property(ω1) if σa(T)\σaw(T) ? π00(T), where σa(T) and σaw(T) denote the approximate point spectrum and the Weyl essential approximate point spectrum of T respectively, and π00(T) = {λ∈ iso σ(T), 0 dim N(T- λI) ∞}. If σa(T)\σaw(T) = π00(T), we say T satisfies property(ω). In this note, we investigate the stability of the property(ω1) and the property(ω) under compact perturbations, and we characterize those operators for which the property(ω1) and the property(ω) are stable under compact perturbations.     

Property(ω_1) and Single Valued Extension Property

In this note we study the property(ω1),a variant of Weyl's theorem by means of the single valued extension property,and establish for a bounded linear operator defined on a Banach space the necessary and sufficient condition for which property(ω1) holds.As a consequence of the main result,the stability of property(ω1) is discussed.     

A NOTE ON n-PERINORMAL OPERATORS

The study of operators satisfying σja(T) = σa(T) is of significant interest. Does σja(T) = σa(T) for n-perinormal operator T ∈ B(H)ff This question was raised by Mecheri and Braha [Oper. Matrices 6(2012), 725–734]. In the note we construct a counterexample to this question and obtain the following result: if T is a n-perinormal operator in B(H), then σja(T)\{0} = σa(T)\{0}. We also consider tensor product of n-perinormal operators.     

A Note on Property(ω)

In this note we study the property(ω),a variant of Weyl's theorem introduced by Rakoevic,by means of the new spectrum.We establish for a bounded linear operator defined on a Banach space a necessary and sufficient condition for which both property(ω) and approximate Weyl's theorem hold.As a consequence of the main result,we study the property(ω) and approximate Weyl's theorem for a class of operators which we call the λ-weak-H(p) operators.     

On the infimum problem of Hilbert space effects

The quantum effects for a physical system can be described by the set ε(H) of positive operators on a complex Hilbert space H that are bounded above by the identity operator I. The infimum problem of Hilbert space effects is to find under what condition the infimum A∧B exists for two quantum effects A and B∈ε(H). The problem has been studied in different contexts by R. Kadison, S. Gudder, M. Moreland, and T. Ando. In this note, using the method of the spectral theory of operators, we give a complete answer of the infimum problem. The characterizations of the existence of infimum A∧B for two effects A. B∈ε(H) are established.     

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.     

渐近纠缠算子单值扩张性质的等价性

算子T∈B(H)称作有单值扩张性质,若对任意一个开集U■C,满足方程(T-λI)f(λ)=0(λ∈U)的唯一的解析函数为零函数.显然,当int σ_p(T)=时,T有单值扩张性质,其中σ_p(T)为T的点谱.本文给出了渐近纠缠算子单值扩张性质的稳定性的等价条件,同时研究了2×2上三角算子矩阵的单值扩张性质的稳定性.     

代数Paranormal算子的谱

若任给x∈H,‖Tx‖~2≤‖T~2x‖·‖x‖,T∈B(H)称为是一个paranormal算子.T∈B(H)称为代数paranormal算子,若存在非常值复值多项式p,使得p(T)为para- normal算子.本文利用代数paranormal算子的谱集的特点,研究了代数paranormal算子以及该算子的拟仿射变换的Weyl型定理.     

关于数值数学的一个典型问题

<正> Collatz L.在综述性文章[1]和[2]中就数值数学的典型问题归纳为五类,第一类是方程Tu=φ或Tu=u的解.关于这类问题主要是寻找解的存在性定理和解的存在区间以及唯一性定理等等. 如所周知,由初始元u_o出发,经过迭代     

An algebraic invariant for Jordan automorphisms on B(H): The set of idempotents

Let H be an infinite dimensional complex Hilbert space. Denote by B(H)the algebra of all bounded linear operators on H, and by I(H) the set of all idempotents in B(H). Suppose that φ is a surjective map from B(H) onto itself. If for everyλ∈ {-1, 1, 2, 3, 1/2, 1/3} and A, B ∈ B(H), A - λB ∈ I(H) (→)φ(A) - λφ(B) ∈ I(H), then φis a Jordan ring automorphism, i.e. there exists a continuous invertible linear or conjugate linear operator T on H such that φ(A) = TAT-1 for all A ∈ B(H), or φ(A) = TA*T-1 for all A ∈ B(H); if, in addition, A - iB ∈ I(H) (→)φ(A) - iφ(B) ∈ I(H), here i is the imaginary unit, then φ is either an automorphism or an anti-automorphism.     

一致Fredholm指标算子及广义(ω′)性质

本文给出了一致Fredholm指标算子的定义及判定,同时定义了Weyl型定理的一种新变化:广义(ω')性质.根据一致Fredholm指标性质定义出一种新的谱集,通过该谱集给出了Hilbert空间上有界线性算子满足广义(ω')性质的充要条件,并且研究了广义(ω')性质的摄动,还研究了算子的亚循环性和广义(ω')性质之间的关系.     

3×3上三角算子矩阵的Weyl型定理

设A∈B(H1),B∈B(H2),C∈B(H3)为给定的三个算子,用M(D,E,F)= 表示一个作用在H1(?)H2(?)H3上的3×3算子矩阵．本文首先给出存在算子D∈B(H2,H1),E∈B(H3,H1),F∈B(H3,H2),使得M(D,E,F)为上半Fredholm算子(下半Fredholm算子)的充要条件．同时研究了3×3算子矩阵 M(D,E,F)的Weyl定理,α-Weyl定理,Browder定理和α-Browder定理．     

多圆柱上Bergman空间到Bloch空间的复合算子

设qo是单位多圆柱Dn到自身的—个全纯映射,ψ是Dn上的—个全纯函数．本文研究单位多圆柱上从Bergman空间Ap（Dn）到Bloch空间β（Dn）的加权复合算子Tψ,ψ通过全纯映射ψ和全纯函数ψ的函数特征。分别给出了单位多圆柱上从Bergman空间AP（Dn）到Bloch空间β（Dn）的加权复合算子Tψ,ψ有界性和紧性的充分必要条件．