性质$(\omega)$的注解

In this note we study the property （ω）, a variant of Weyl＇s theorem introduced by Rakocevic, 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.     

$(\omega')$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.     

$(\omega_1)$性质与单值延拓性质

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.     

$(\omega)$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.     

The Equivalence between Property (ω) and Weyl’s Theorem

We call T ∈ B(H) consistent in Fredholm and index (briefly a CFI operator) if for each B ∈ B(H),T B 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 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.     

k-拟-*-A(ｎ)算子的性质(英文)

An operator T is called k-quasi-*-A（n） operator, if T^*k|T¹⁺ⁿ|^2/（1+n）T^k ≥T^*k|T^* |²T^k , k ∈ Z, which is a generalization of quasi-*-A（n） operator. In this paper we prove some properties of k-quasi-*-A（n） operator, such as, if T is a k-quasi-*-A（n） operator and N（T ）■N（T^* ）, then its point spectrum and joint point spectrum are identical. Using these results, we also prove that if T is a k-quasi-*-A（n） operator and N（T ）■N（T ）, then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.     

理想上的广义$(\theta,\phi)$-导子的正交性

In this paper,necessary and sufficient conditions concerning the orthogonality and the composition of a couple of generalized （θ,φ）-derivations on a nonzero ideal of a semiprime ring are presented.These results are generalizations of several results of Breˇsar and Vukman,which are related to a theorem of Posner on the product of two derivations on a prime ring.     

对性质(ω)等价性的研究

性质(ω)是Weyl定理的一种变形.文章中将算子的一致Fredholm指标性质用于性质(ω)的判定中.根据一致Fredholm指标性质定义出一种新的谱集,通过该谱集和算子的拓扑一致降标之间的关系,给出了有界线性算子与其共轭算子同时满足性质(ω)的充要条件.之后,研究了算子矩阵的(ω)性质.     

关于一类复值大数的积分（英）

Here presented are two limit theorems for a kind of integrals involvingcomplex-valued functions of large numbers. The form of integrals may be regardedas a natural generalization of those integrals occured in the probability limit theoremsof Chung and Erds. Our main result is Theorem 2 whose Proof rests upon some knownresults of [1] and makes an extentive use of Bonnet's second mean value theorem andrelated analytic techniques.     

强正则 $(\alpha,\beta)$-族和平移强正则 $(\alpha,\beta)$-几何

本文给出了强正则$(\alpha,\beta)-$族的概念,它是[4]和[5]中$SPG-$族概念的推广.进一步,给出了一种用强正则 $(\alpha,\beta)-$族构造强正则$(\alpha,\beta)-$几何的方法.另外,本文还证明了由强正则$(\alpha,\beta)-$线汇构造的强正则$(\alpha,\beta)-$几何是平移强正则$(\alpha,\beta)-$几何;当$t-r>\beta$时,反之亦成立.     

广义(ω)性质及亚循环算子

研究了Weyl定理的一种变化形式:广义$(\omega)$性质; 给出了广义$(\omega)$性质成立的充要条件.同时, 广义$(\omega)$性质及算子的亚(超)循环性之间的关系得到了研究.     

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．     

Browder定理和Weyl定理

本文通过定义两个新的谱集,给出了Browder定理和Weyl定理对算子T以及f(T)成立的充要条件,其中f∈H(σ(T)),H(σ(T))表示在谱集σ(T)的开邻域上解析的函数的全体。     

关于空间$S(\Omega,\Sigma,\mu)$与$L^\beta(\Omega,\Sigma,\mu)$上的次加上半连续$\alpha$-正齐性泛函

本文得到了$S(\Omega,\Sigma,\mu)$和$L^\beta(\Omega,\Sigma,\mu)$分别不存在非零的上半连续、次加、$\alpha$-正齐性泛函(分别有本文得到了$S(\Omega,\Sigma,\mu)$和$L^\beta(\Omega,\Sigma,\mu)$分别不存在非零的上半连续、次加、$\alpha$-正齐性泛函(分别有本文得到了$S(\Omega,\Sigma,\mu)$和$L^\beta(\Omega,\Sigma,\mu)$分别不存在非零的上半连续、次加、$\alpha$-正齐性泛函(分别有本文得到了S（Ω，∑，μ）与L^β（Ω，∑，μ）分别不存在非零的上半连续、次加、α-正齐性泛函（分别有0≤α≤1和β〈α≤1）的充要条件．     

An Equivalent Characterization of $CMO(\mathbb{R}^n)$ with $A_p$ Weights

Let $1相似文献