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1.
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.  相似文献   

2.
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.  相似文献   

3.
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.  相似文献   

4.
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.  相似文献   

5.
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   

6.
On the Equivalence and Generalized of Weyl Theorem Weyl Theorem   总被引:3,自引:0,他引:3  
We know that an operator T acting on a Banach space satisfying generalized Weyl's theorem also satisfies Weyl's theorem. Conversely we show that if all isolated eigenvalues of T are poles of its resolvent and if T satisfies Weyl's theorem, then it also satisfies generalized Weyl's theorem. We give also a sinlilar result for the equivalence of a-Weyl's theorem and generalized a-Weyl's theorem. Using these results, we study the case of polaroid operators, and in particular paranormal operators.  相似文献   

7.
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.  相似文献   

8.
E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder's theorem, Rothe's theorem, Altman's theorem, Petryshyn's theorem, etc.  相似文献   

9.
Let T be a Banach space operator, E(T) be the set of all isolated eigenvalues of T and π(T) be the set of all poles of T. In this work, we show that Browder's theorem for T is equivalent to the localized single-valued extension property at all complex numbers λ in the complement of the Weyl spectrum of T, and we give some characterization of Weyl's theorem for operator satisfying E(T) = π(T). An application is also given.  相似文献   

10.
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.  相似文献   

11.
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.  相似文献   

12.
In this article, we generalize and simplify the proof of the Takesaki-Takai $\gamma $-duality theorem. Assume a morphism \textbf{\textit{$\omega \; :\; G\to Aut\left({\rm A}\right)$}} is a projective representation of the locally compact Abel group \textbf{\textit{$G$}} in \textbf{\textit{$Aut\left({\rm A}\right)$}}, mapping $\gamma \; :\; G\to G$ is continuous, and $\left({\rm A},\; G,\; \omega \right)$ is a dynamic system then there exists isomorphism \[\Upsilon \; :\; Env_{\hat{\omega }} {}^{\gamma } \left(L^{1} \left(\hat{G},\; Env_{\omega } {}^{\gamma } \left(L^{1} \left(G,\; {\rm A}\right)\right)\right)\right)\to {\rm A}\otimes LK\left(L^{2} \left(G\right)\right) \] which is the equivariant for the double dual action \[\hat{\hat{\omega }}\; :\; G\to Aut\left(Env_{\hat{\omega }} {}^{\gamma } \left(L^{1} \left(\hat{G},\; Env_{\omega } {}^{\gamma } \left(L^{1} \left(G,\; {\rm A}\right)\right)\right)\right)\right).\] These results deepen our understanding of the representation theory and are especially interesting given their possible applications to problems of the quantum theory.  相似文献   

13.
若对x∈H,‖Tx‖~2≤‖T~2x‖‖x‖,则称T是仿正规算子.d_(AB)表示δ_(AB)或△_(AB),其中δ_(AB)和△_(AB)分别表示Banach空间B(H)上的广义导算子和初等算子,其定义为δ_(AB)X=AX-XB,△_(AB)X=AXB-X,X∈B(H).若A和B~*是仿正规算子,则可证d_(AB)是polaroid算子,f∈H(σ(d_(AB))),f(d_(AB))满足广义Weyl定理,f(d_(AB)~*)满足广义a-Weyl定理,其中H(σ(d_(AB)))表示在σ(d_(AB))的某邻域上解析的函数全体.  相似文献   

14.
In this paper we introduce the notion of (f,ω)-compatible pair (B,H), by which we construct a Hopf algebra in the category HHYD of Yetter-Drinfeld H-modules by twisting the comultiplication of B. We also study the property of ω-smash coproduct Hopf algebras Bω H.  相似文献   

15.
若T或T~*是无穷维可分的Hilbert空间H上的代数κ-拟-A类算子,则Weyl定理对任意的f∈H(σ(T))成立,其中H(σ(T))为σ(T)的开邻域上解析函数的全体.若T~*是代数κ-拟-A类算子,则a-Weyl定理对f(T)成立。还证明了若T或T~*是代数κ-拟-A类算子,则Weyl谱与本质近似点谱的谱映射定理对f(T)成立.  相似文献   

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