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1.
If is a upper triangular matrix on the Hilbert space , then -Weyl's theorem for and need not imply -Weyl's theorem for , even when . In this note we explore how -Weyl's theorem and -Browder's theorem survive for operator matrices on the Hilbert space. 相似文献
2.
A Banach space operator T∈ B( X) may be said to be “consistent in invertibility” provided that for each S∈ B( X), TS and ST are either both or neither invertible. The induced spectrum contributes the conditions equivalent to various forms of “Weyl's theorem”. 相似文献
3.
The Kato spectrum of an operator is deployed to give necessary and sufficient conditions for Browder's theorem to hold. 相似文献
4.
For A∈ B( X), B∈ B( Y) and C∈ B( Y, X), let MC be the operator defined on X⊕ Y by . In this paper, we study defect set ( Σ( A)∪ Σ( B))? Σ( MC), where Σ is the Browder spectrum, the essential approximate point spectrum and Browder essential approximate point spectrum. We then give application for Weyl's and Browder's theorems. 相似文献
5.
When and are given we denote by an operator acting on the Banach space of the form In this note we examine the relation of Weyl's theorem for and through local spectral theory. 相似文献
6.
In this paper it is shown that if is a upper triangular operator matrix acting on the Hilbert space and if denotes the ``Weyl spectrum", then the passage from to is accomplished by removing certain open subsets of from the former, that is, there is equality where is the union of certain of the holes in which happen to be subsets of . 相似文献
7.
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
8.
``Weyl's theorem holds" for an operator on a Banach space when the complement in the spectrum of the ``Weyl spectrum" coincides with the isolated points of spectrum which are eigenvalues of finite multiplicity. This is close to, but not quite the same as, equality between the Weyl spectrum and the ``Browder spectrum", which in turn ought to, but does not, guarantee the spectral mapping theorem for the Weyl spectrum of polynomials in . In this note we try to explore these distinctions. 相似文献
9.
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
10.
When A∈ B( H) and B∈ B( K) are given, we denote by MC the operator acting on the infinite dimensional separable Hilbert space H⊕ K of the form . In this paper, we prove that
11.
``Polaroid elements" represent an attempt to abstract part of the condition, ``Weyl's theorem holds" for operators. 相似文献
12.
Let X and Y be given Banach spaces. For A∈ B( X), B∈ B( Y) and C∈ B( Y, X), let MC be the operator defined on X⊕ Y by . In this paper we give conditions for continuity of τ at MC through continuity of τ at A and B, where τ can be equal to the spectrum or approximate point spectrum. 相似文献
13.
A bounded linear operator on a Banach space is said to satisfy ``Weyl's theorem' if the complement in the spectrum of the Weyl spectrum is the set of all isolated points of the spectrum which are eigenvalues of finite multiplicity. In this paper we show that if is a paranormal operator on a Hilbert space, then satisfies Weyl's theorem for every algebraic operator which commutes with . 相似文献
14.
In this note it is shown that if is an ``algebraically hyponormal" operator, i.e., is hyponormal for some nonconstant complex polynomial , then for every , Weyl's theorem holds for , where denotes the set of analytic functions on an open neighborhood of . 相似文献
15.
Two variants of the Weyl spectrum are discussed. We find, for example, that if one of them coincides with the Browder spectrum then Weyl's theorem holds, and conversely for isoloid operators. 相似文献
16.
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
17.
In this note we consider Weyl's theorem and Browder's theorem in several variables. The main result is as follows. Let T be a doubly commuting n-tuple of hyponormal operators acting on a complex Hilbert space. If T has the quasitriangular property, i.e., the dimension of the left cohomology for the Koszul complex Λ( T− λ) is greater than or equal to the dimension of the right cohomology for Λ( T− λ) for all λ∈ Cn, then ‘Weyl's theorem’ holds for T, i.e., the complement in the Taylor spectrum of the Taylor Weyl spectrum coincides with the isolated joint eigenvalues of finite multiplicity. 相似文献
18.
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. 相似文献
19.
The transmission of “Weyl's theorem” from operators on Banach spaces to their tensor products, and also to their associated multiplication operators, is deconstructed. 相似文献
20.
When A∈ B( H) and B∈ B( K) are given, we denote by MC the operator acting on the infinite-dimensional separable Hilbert space H⊕ K of the form . In this paper, it is shown that there exists some operator C∈ B( K, H) such that MC is upper semi-Fredholm and ind( MC)?0 if and only if there exists some left invertible operator C∈ B( K, H) such that MC is upper semi-Fredholm and ind( MC)?0. A necessary and sufficient condition for MC to be upper semi-Fredholm and ind( MC)?0 for some C∈Inv( K, H) is given, where Inv( K, H) denotes the set of all the invertible operators of B( K, H). In addition, we give a necessary and sufficient condition for MC to be upper semi-Fredholm and ind( MC)?0 for all C∈Inv( K, H). 相似文献
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