Characterizations of perturbations of spectra of 2×2 upper triangular operator matrices
Characterizations of perturbations of spectra of 2×2 upper triangular operator matrices
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DOI：
10.1016/j.jmaa.2012.03.031
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发表时间：
2012-08
影响因子：
1.3
通讯作者：
Shifang Zhang;Zhaoqi Wu
中科院分区：
文献类型：
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作者：
Shifang Zhang;Zhaoqi Wu
当给定A∈B(H)和B∈B(K)时，我们用MC表示作用在无限维可分Hilbert空间H⊕K上的算子MC=(AC0B)。本文首先给出了一类C-∈B(K，H)的MCTO是左可逆算子(上半Weyl，上半Fredholm型)算子的一些充要条件，推广了Cao等人的相应结果。(2006)[4]，曹和孟(2005)[5]，Hwang和Lee(2001)[12]，Li和Du(2006)[15]。然后我们给出了一些反例。
When A∈B(H) and B∈B(K) are given, we denote by MCthe operator acting on the infinite dimensional separable Hilbert space H⊕K of the form MC=(AC0B). In this paper, we first give some necessary and sufficient conditions for MCto be a left invertible operator (an upper semi-Weyl, upper semi-Fredholm) operator for some C∈B(K,H), which extend the corresponding results in Cao et al. (2006) [4], Cao and Meng (2005) [5], Hwang and Lee (2001) [12] and Li and Du (2006) [15]. Then we present some counter-examples.