共查询到20条相似文献,搜索用时 538 毫秒
1.
This paper studies Weyl's theorems, and some related results for operators with Dunford's property (C). Weyl's theorem in some classes of operators (e.g.M-hyponormal,p-hyponormal and totally paranormal operators) is considered. 相似文献
2.
Xiaohong Cao 《Journal of Mathematical Analysis and Applications》2006,320(2):795-803
Using the new spectrum set defined in this note, we give the necessary and sufficient condition for T which the Weyl's theorem holds. We also consider how the Weyl's theorem survives for analytically Class A operators. 相似文献
3.
Weyl's theorem for operator matrices 总被引:11,自引:0,他引:11
Woo Young Lee 《Integral Equations and Operator Theory》1998,32(3):319-331
Weyl's theorem holds for an operator when the complement in the spectrum of the Weyl spectrum coincides with the isolated points of the spectrum which are eigenvalues of finite multiplicity. By comparison Browder's theorem holds for an operator when the complement in the spectrum of the Weyl spectrum coincides with Riesz points. Weyl's theorem and Browder's theorem are liable to fail for 2×2 operator matrices. In this paper we explore how Weyl's theorem and Browder's theorem survive for 2×2 operator matrices on the Hilbert space.Supported in part by BSRI-97-1420 and KOSEF 94-0701-02-01-3. 相似文献
4.
Mourad Oudghiri 《Integral Equations and Operator Theory》2005,53(4):535-545
In the present paper we examine the stability of Weyl’s theorem under perturbations. We show that if T is an isoloid operator on a Banach space, that satisfies Weyl’s theorem, and F is a bounded operator that commutes with T and for which there exists a positive integer n such that Fn is finite rank, then T + F obeys Weyl’s theorem. Further, we establish that if T is finite-isoloid, then Weyl’s theorem is transmitted from T to T + R, for every Riesz operator R commuting with T. Also, we consider an important class of operators that satisfy Weyl’s theorem, and we give a more general perturbation results
for this class. 相似文献
5.
6.
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. 相似文献
7.
In this note we study the property(ω),a variant of Weyl's theorem introduced by Rakoevic,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. 相似文献
8.
In this note we study the property (w), a variant of Weyl's theorem introduced by Rako?evi?, by means of the localized single-valued extension property (SVEP). We establish for a bounded linear operator defined on a Banach space several sufficient and necessary conditions for which property (w) holds. We also relate this property with Weyl's theorem and with another variant of it, a-Weyl's theorem. We show that Weyl's theorem, a-Weyl's theorem and property (w) for T (respectively T*) coincide whenever T* (respectively T) satisfies SVEP. As a consequence of these results, we obtain that several classes of commonly considered operators have property (w). 相似文献
9.
10.
关于广义Aluthge变换的谱性质的研究 总被引:2,自引:0,他引:2
设T∈H(H),T=U|T|是算子T的极分解,则定义T^λ=|T|^λU|T|^1-λ和T^λ(*)=|T*|^λU|T*|^1-λ,(其中0〈λ〈1)分别为算子的广义Aluthge变换和广义*-Aluthge变换.本文中主要研究了三者之间的几种谱的关系.同时,还证明了算子T满足修正的Weyl定理当且仅当弘满足修正的Weyl定理当且仅当T^λ(*)满足修正的Weyl定理.最后证明了算子T满足a—Weyl定理当且仅当T^λ满足a—Weyl定理. 相似文献
11.
3×3上三角算子矩阵的Weyl型定理 总被引:1,自引:0,他引:1
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. 相似文献
12.
In this paper, we prove an intersection theorem for an infinite family of correspondences defined on non-compact spaces, and apply this result to give a new generalization of the Yannelis–Prabhakar existence theorem for equilibrium of abstract economies. 相似文献
13.
Generalized Browder’s Theorem and SVEP 总被引:1,自引:0,他引:1
A bounded operator
a Banach space, is said to verify generalized Browder’s theorem if the set of all spectral points that do not belong to the
B-Weyl’s spectrum coincides with the set of all poles of the resolvent of T, while T is said to verify generalized Weyl’s theorem if the set of all spectral points that do not belong to the B-Weyl spectrum
coincides with the set of all isolated points of the spectrum which are eigenvalues. In this article we characterize the bounded
linear operators T satisfying generalized Browder’s theorem, or generalized Weyl’s theorem, by means of localized SVEP, as well as by means
of the quasi-nilpotent part H
0(λI − T) as λ belongs to certain subsets of
. In the last part we give a general framework for which generalized Weyl’s theorem follows for several classes of operators. 相似文献
14.
A. Amini-Harandi 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(12):4661-4665
In this paper, we first prove some generalizations of Caristi’s fixed point theorem. Then we give some applications to the fixed point theory of weakly contractive set-valued maps and the minimization problem. 相似文献
15.
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. 相似文献
16.
Let H be a complex separable infinite dimensional Hilbert space. In this paper, a variant of the Weyl spectrum is discussed. Using the new spectrum, we characterize the necessary and sufficient conditions for both T and f(T) satisfying Weyl's theorem, where f ∈ Hol(σ(T)) and Hol(σ(T)) is defined by the set of all functions f which are analytic on a neighbourhood of σ(T) and are not constant on any component of σ(T). Also we consider the perturbations of Weyl's theorem for f(T). 相似文献
17.
18.
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. 相似文献
19.
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. 相似文献
20.
Robin Fellgett 《Monatshefte für Mathematik》1979,87(3):209-228
A class of minimal actions of finitely generated abelian groups is constructed. The class contains many non-trivial actions with quasi discrete spectrum and is used to give an ergodic theoretic proof of Weyl's theorem on uniform distribution of polynomials of finitely many variables. 相似文献