The Decomposability for Operator Matrices and Perturbations  

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作  者:Xiao Li WANG ALATANCANG 

机构地区:[1]School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,P.R.China [2]Statistics and Mathematics College,Inner Mongolia University of Finance and Economics,Hohhot 010070,P.R.China [3]Mathematics Science College,Inner Mongolia Normal University,Hohhot 010022,P.R.China

出  处:《Acta Mathematica Sinica,English Series》2023年第3期497-512,共16页数学学报(英文版)

基  金:Supported by National Natural Science Foundation of China(Grant No.11761029);Inner Mongolia Higher Education Science and Technology Research Project(Grant Nos.NJZY22323 and NJZY22324);Inner Mongolia Natural Science Foundation(Grant No.2018MS07020)。

摘  要:Let X and Y be Banach spaces.For A∈L(X),B∈L(Y),C∈L(Y,X),let MCbe the operator matrix defined on X⊕Y by M_(C)=(AC0B)∈L(X⊕Y).In this paper we investigate the decomposability for MC.We consider Bishop’s property(β),decomposition property(δ)and Dunford’s property(C)and obtain the relationship of these properties between M_(C) and its entries.We explore how σ_(*)(M_(C))shrinks from σ_(*)(A)∪σ_(*)(B),where σ_(*)denotes σ_(β),σ_(δ),σ_(C),σ_(dec).In particular,we develop some sufficient conditions for equality σ_(*)(MC)=σ_(*)(A)∪σ_(*)(B).Besides,we consider the perturbation of these properties for MCand show that in perturbing with certain operators C the properties for MCkeeps with A,B.Some examples are given to illustrate our results.Furthermore,we study the decomposability for(0AB0).Finally,we give applications of decomposability for operator matrices.

关 键 词:Bishop’s property(β) decomposition property(δ) Dunford’s property(C) DECOMPOSABILITY operator matrix PERTURBATION local spectral theory 

分 类 号:O177[理学—数学]

 

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