共查询到20条相似文献,搜索用时 0 毫秒
1.
Bhaggy Duggal Robin Harte In Ho Jeon 《Proceedings of the American Mathematical Society》2004,132(5):1345-1349
``Polaroid elements" represent an attempt to abstract part of the condition, ``Weyl's theorem holds" for operators.
2.
Robin Harte 《Journal of Mathematical Analysis and Applications》2007,336(2):1124-1131
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
3.
Xiaohong Cao Maozheng Guo Bin Meng 《Proceedings of the American Mathematical Society》2005,133(10):2977-2984
The Kato spectrum of an operator is deployed to give necessary and sufficient conditions for Browder's theorem to hold.
4.
Another note on Weyl's theorem 总被引:24,自引:0,他引:24
``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.
5.
B.P. Duggal 《Journal of Mathematical Analysis and Applications》2007,335(2):990-995
Necessary and sufficient conditions for hypercyclic/supercyclic Banach space operators T to satisfy are proved. 相似文献
6.
Derek Kitson Carlos Hernández 《Journal of Mathematical Analysis and Applications》2011,378(1):128-132
Approximately fifty percent of Weyl's theorem fails to transfer from Hilbert space operators to their tensor product. As a biproduct we find that the product of circles in the complex plane is a limaçon. 相似文献
7.
Pietro Aiena Jesú s R. Guillen 《Proceedings of the American Mathematical Society》2007,135(8):2443-2451
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 .
8.
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 .
9.
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
10.
Consistent invertibility and Weyl's theorem 总被引:1,自引:0,他引:1
Xiaohong Cao Hejia Zhang Yanhua Zhang 《Journal of Mathematical Analysis and Applications》2010,369(1):258-264
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
11.
A Banach space operator T satisfies Weyl's theorem if and only if T or T∗ has SVEP at all complex numbers λ in the complement of the Weyl spectrum of T and T is Kato type at all λ which are isolated eigenvalues of T of finite algebraic multiplicity. If T∗ (respectively, T) has SVEP and T is Kato type at all λ which are isolated eigenvalues of T of finite algebraic multiplicity (respectively, T is Kato type at all λ∈isoσ(T)), then T satisfies a-Weyl's theorem (respectively, T∗ satisfies a-Weyl's theorem). 相似文献
12.
Weyl spectra and Weyl's theorem 总被引:1,自引:0,他引:1
Xiaohong Cao Maozheng Guo Bin Meng 《Journal of Mathematical Analysis and Applications》2003,288(2):758-767
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
13.
Raúl E. Curto Young Min Han 《Journal of Mathematical Analysis and Applications》2007,336(2):1424-1442
We find necessary and sufficient conditions for a Banach space operator T to satisfy the generalized Browder's theorem. We also prove that the spectral mapping theorem holds for the Drazin spectrum and for analytic functions on an open neighborhood of σ(T). As applications, we show that if T is algebraically M-hyponormal, or if T is algebraically paranormal, then the generalized Weyl's theorem holds for f(T), where f∈H((T)), the space of functions analytic on an open neighborhood of σ(T). We also show that if T is reduced by each of its eigenspaces, then the generalized Browder's theorem holds for f(T), for each f∈H(σ(T)). 相似文献
14.
H. Zguitti 《Journal of Mathematical Analysis and Applications》2006,316(1):373-381
We prove that if either T or T∗ has the single-valued extension property, then the spectral mapping theorem holds for B-Weyl spectrum. If, moreover T is isoloid, and generalized Weyl's theorem holds for T, then generalized Weyl's theorem holds for f(T) for every f∈H(σ(T)). An application is given for algebraically paranormal operators. 相似文献
15.
Young Min Han 《Journal of Mathematical Analysis and Applications》2010,370(2):538-542
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
16.
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 a 2×2 operator matrix MC is upper semi-Fredholm and ind(MC)?0 for some C∈B(K,H) if and only if A is upper semi-Fredholm and
17.
A note on Weyl's theorem for operator matrices 总被引:5,自引:0,他引:5
Slavisa V. Djordjevic Young Min Han 《Proceedings of the American Mathematical Society》2003,131(8):2543-2547
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.
In this note we examine the relation of Weyl's theorem for and through local spectral theory.
18.
B. P. Duggal 《Proceedings of the American Mathematical Society》2007,135(9):2899-2905
A Banach space operator is completely hereditarily normaloid, , if either every part, and (also) for every invertible part , of is normaloid or if for every complex number every part of is normaloid. Sufficient conditions for the perturbation of by an algebraic operator to satisfy Weyl's theorem are proved. Our sufficient conditions lead us to the conclusion that the conjugate operator satisfies -Weyl's theorem.
19.
Xiaohong Cao 《Proceedings of the American Mathematical Society》2007,135(6):1701-1708
In this note, the relation between hypercyclic operator matrices (or supercyclic operator matrices) and the operator matrices which satisfy Weyl type theorems is discussed. Also, using a variant of the essential approximate point spectrum, we give the necessary and sufficient conditions for for which a-Browder's theorem or a-Weyl's theorem holds.
20.
The main objective of this work is to study generalized Browder's and Weyl's theorems for the multiplication operators LA and RB and for the elementary operator τAB=LARB. 相似文献