Drazin spectrum of operator matrices on the Banach space
Drazin spectrum of operator matrices on the Banach space
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DOI：
10.1016/j.laa.2008.06.002
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发表时间：
2008-10
影响因子：
1.1
通讯作者：
Shifang Zhang;H. Zhong;Qiaofen Jiang
中科院分区：
文献类型：
--
作者：
Shifang Zhang;H. Zhong;Qiaofen Jiang
当A∈B（X）和B∈B（Y）已知时，我们用MC表示作用在Banach空间X <$Y上的MC= AC_（0 B）型算子.本文得出并证明了对于给定的算子对（A，B），σD（A）<$σD（B）=σD（MC）<$W对每个C∈B（Y，X）成立，其中W是σD（MC）中某些洞的并，这些洞恰好是σD（A）<$σD（B）的子集.此外，还研究了集合B（Y，X）σD（MC），并给出了一个例子.
When A∈B(X) and B∈B(Y) are given, we denote by MCthe operator acting on the Banach space X⊕Y of the form MC=AC0B. In this paper, it is concluded and proved that for a given pair (A,B) of operators, σD(A)∪σD(B)=σD(MC)∪W holds for every C∈B(Y,X), where W is the union of certain holes in σD(MC), which happen to be subsets of σD(A)∩σD(B). Moreover, the set ⋂C∈B(Y,X)σD(MC) is investigated and an example for it is considered.