drazin spectrum
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Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3191-3204
Author(s):  
Ju An ◽  
Eungil Ko ◽  
Ji Lee

We denote the collection of the 2 x 2 operator matrices with (1,2)-entries having closed range by S. In this paper, we study the relations between the operator matrices in the class S and their component operators in terms of the Drazin spectrum and left Drazin spectrum, respectively. As some application of them, we investigate how the generalized Weyl?s theorem and the generalized a-Weyl?s theorem hold for operator matrices in S, respectively. In addition, we provide a simple example about an operator matrix in S satisfying such Weyl type theorems.



2019 ◽  
Vol 38 (3) ◽  
pp. 63-69
Author(s):  
Abdelaziz Tajmouati ◽  
Hamid Boua

Let $(T(t))_{t\geq 0}$ be a $C_0$ semigroup of bounded linear operators on a Banach space $X$ and denote its generator by $A$. A fundamental problem to decide whether the Drazin spectrum of each operator $T(t)$ can be obtained from the Drazin spectrum of $A$. In particular, one hopes that the Drazin Spectral Mapping Theorem holds, i.e., $e^{t \sigma_{D}(A)}=\sigma_{D}(T(t))\backslash \{0\}$ for all $t \geq 0$.



2014 ◽  
Vol 29 (2) ◽  
pp. 162-170 ◽  
Author(s):  
Shi-fang Zhang ◽  
Huai-jie Zhong ◽  
Li-qiong Lin


2008 ◽  
Vol 429 (8-9) ◽  
pp. 2067-2075 ◽  
Author(s):  
Shifang Zhang ◽  
Huaijie Zhong ◽  
Qiaofen Jiang


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