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1.
Browder spectra for upper triangular operator matrices 总被引:1,自引:0,他引:1
Xiaohong Cao 《Journal of Mathematical Analysis and Applications》2008,342(1):477-484
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
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Browder spectra of upper-triangular operator matrices 总被引:1,自引:0,他引:1
Let be a 2×2 upper triangular operator matrix acting on the Hilbert space H⊕K. In this paper, for given operators A and B, we prove that
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Salma Charfi Aref Jeribi Rihab Moalla 《Mathematical Methods in the Applied Sciences》2014,37(4):597-608
The main goal of this paper is to give a characterization of Wolf, Schechter, and Browder essential spectra of (2 × 2) matrix operator on a Banach space. Furthermore, we apply the obtained results to transport equations. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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This paper is concerned with the spectral properties of the unbounded upper triangular operator matrix with diagonal domain. Some sufficient and necessary conditions are given under which the essential spectrum, the Weyl spectrum and the Browder spectrum of such operator matrix, respectively, coincide with the union of the essential spectrum, the Weyl spectrum and the Browder spectrum of its diagonal entries. 相似文献
6.
When A∈B(H) and B∈B(K) are given, we denote by MC the operator acting on the Hilbert space H⊕K of the form . In this note, it is shown that the following results in [Hai-Yan Zhang, Hong-Ke Du, Browder spectra of upper-triangular operator matrices, J. Math. Anal. Appl. 323 (2006) 700-707]
7.
Weyl spectra of operator matrices 总被引:1,自引:0,他引:1
Woo Young Lee 《Proceedings of the American Mathematical Society》2001,129(1):131-138
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 .
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设算子S和T拟相似,应用算子谱的精密结构的分析,证明了Browder本质谱σB(S)的连通分支与σB(T)的某些子集的相交关系以及左本质谱σle(S)的连通分支与本质谱σe(T)的某些子集的相交关系,给出左本质谱σle(S)的连通分支与σle(T)相交的充分条件和充要条件. 相似文献
9.
Spectra of upper triangular operator matrices 总被引:4,自引:0,他引:4
C. Benhida E. H. Zerouali H. Zguitti 《Proceedings of the American Mathematical Society》2005,133(10):3013-3020
Let be given Banach spaces. For and , let be the operator defined on by . We give sufficient conditions on to get where runs over a large class of spectra. We also discuss the case of some spectra for which the latter equality fails.
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苏维钢 《应用泛函分析学报》2006,8(3):284-288
利用算子谱的精密结构的分析方法,给出算子S和T拟相似时Kato本质谱σK(S)的一个连通分支与σK(T)相交的充分条件和充要条件,同时证明了Browder本质谱σB(S)的每一个连通分支与Kato本质谱σK(T)的某些子集的交集是非空的. 相似文献
11.
In the present paper, we define the S-left and the S-right essential spectra of a linear operator and we study the stability of the S-essential spectra on a Banach space. 相似文献
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Eungil Ko 《Linear and Multilinear Algebra》2019,67(6):1198-1216
13.
Young Min Han Slavisa V. Djordjevic 《Proceedings of the American Mathematical Society》2002,130(3):715-722
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.
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Let A ∈ B(X) and B ∈ B(Y), MC be an operator on Banach space X ⊕ Y given A C by MC =A generalized Drazin spectrum defined by σgD(T) = {λ∈ C : T-0 BλI is not generalized Drazin invertible} is considered in this paperIt is shown thatσgD(A) ∪σgD(B) = σgD(MC) ∪ WgD(A, B, C),where WgD(A, B, C) is a subset of σgD(A) ∩σgD(B) and a union of certain holes in σgD(MC).Furthermore, several sufficient conditions for σgD(A) ∪σgD(B) = σgD(MC) holds for every C ∈ B(Y, X) are given. 相似文献
16.
Marwa Belghith Nedra Moalla Ines Walha 《Mathematical Methods in the Applied Sciences》2017,40(18):7218-7230
We define an abstract setting to treat essential spectra of unbounded coupled operator matrix. We prove a well‐posedness result and develop a spectral theory which also allows us to prove an amelioration to many earlier works. We point out that a concrete example from integro‐differential equation fit into this abstract framework involving a general class of regular operator in L1 spaces. 相似文献
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For any triangular operator matrix acting in a direct sum of complex Banach spaces, the order of a pole of the resolvent (i.e. the index) is determined as a function of the coefficients in the Laurent series for all the (resolvents of the) operators on the diagonal and of the operators below the diagonal. This result is then applied to the case of certain nonnegative operators in Banach lattices. We show how simply these results imply the Rothblum Index Theorem (1975) for nonnegative matrices. Finally, examples for calculating the index are presented.
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T. Kh. Rasulov 《Russian Mathematics (Iz VUZ)》2008,52(12):50-59
In this paper we consider a model operator which acts in a three-particle cut subspace of the Fock space. We describe “two-particle” and “three-particle” branches of the essential spectrum and obtain an analog of the Faddeev equation for eigenfunctions of this operator. 相似文献
20.
On K_0-groups of operator algebras on Banach spaces 总被引:1,自引:0,他引:1
ZHANG Yunnan ZHONG Huaijie & SU Weigang School of Mathematics Computer Science Fujian Normal University Fuzhou China 《中国科学A辑(英文版)》2006,49(2)
This paper merges some classifications of G-M-type Banach spaces simplifically, discusses the condition of K0(B(X)) = 0 for operator algebra B(X) on a Banach space X, and obtains a result to improve Laustsen's sufficient condition, gives an example to show that X ≈ X2 is not a sufficient condition of K0(B(X)) = 0. 相似文献