By the new spectrum originated from the single-valued extension property,we give the necessary and sufficient conditions for a bounded linear operator defined on a Banach space for which property(ω)holds.Meanwhile,th...By the new spectrum originated from the single-valued extension property,we give the necessary and sufficient conditions for a bounded linear operator defined on a Banach space for which property(ω)holds.Meanwhile,the relationship between hypercyclic property(or supercyclic property)and property(ω)is discussed.展开更多
设M_R=(T R O S)是定义在Banach空间X⊕Y上的2×2上三角算子矩阵,则T和S满足性质(gw)(或性质(gb))推不出M_R满足性质(gw)(或性质(gb)),即使R=0.文章主要利用局部谱理论的知识,研究了Banach空间上2×2上三角算子矩阵在什么情况...设M_R=(T R O S)是定义在Banach空间X⊕Y上的2×2上三角算子矩阵,则T和S满足性质(gw)(或性质(gb))推不出M_R满足性质(gw)(或性质(gb)),即使R=0.文章主要利用局部谱理论的知识,研究了Banach空间上2×2上三角算子矩阵在什么情况下满足性质(gb)和性质(gw).展开更多
In this paper, we use the constancy of certain subspace valued mappings on the components of the generalized Kato resolvent set and the equivalences of the single-valued extension property at a point 0 for operators w...In this paper, we use the constancy of certain subspace valued mappings on the components of the generalized Kato resolvent set and the equivalences of the single-valued extension property at a point 0 for operators which admit a generalized Kato decomposition to obtain a classification of the components of the generalized Kato resolvent set of operators. We also give some applications of these results展开更多
Let T be a Banach space operator, E（T） be the set of all isolated eigenvalues of T and π（T） be the set of all poles of T. In this work, we show that Browder＇s theorem for T is equivalent to the localized single-...Let T be a Banach space operator, E（T） be the set of all isolated eigenvalues of T and π（T） be the set of all poles of T. In this work, we show that Browder＇s theorem for T is equivalent to the localized single-valued extension property at all complex numbers λ in the complement of the Weyl spectrum of T, and we give some characterization of Weyl＇s theorem for operator satisfying E（T） = π（T）. An application is also given.展开更多
本文研究了Banach空间中上三角算子矩阵MC(A C 0 B)∈L(X■Y)的局部谱性质,其中A∈L(X),B∈L(Y),C∈L(Y,X),X,Y是无穷维复Banach空间,L(X,Y)表示X到Y的所有有界线性算子.首先考察了MC的单值扩张性,借助于向量值解析函数和解析核等工具...本文研究了Banach空间中上三角算子矩阵MC(A C 0 B)∈L(X■Y)的局部谱性质,其中A∈L(X),B∈L(Y),C∈L(Y,X),X,Y是无穷维复Banach空间,L(X,Y)表示X到Y的所有有界线性算子.首先考察了MC的单值扩张性,借助于向量值解析函数和解析核等工具给出了集合S(MC)={λ∈C:MC在λ没有单值扩张性}的刻画,并得到对任意C∈L(Y,X)等式S(MC)=S(A)∪S(B)都成立的条件.进一步,研究了MC的单值扩张性扰动,得到了对于给定A∈L(X),B∈L(Y),等式S(MC)=S(A)∪(B)成立时C所需的条件.同时,举例说明了这些条件的合理性.最后,把所得结果运用到上三角算子矩阵的谱和局部谱上,得到了σ(MC)=σ(A)∪σ(B)和σMMC(x■0)=σA(x)成立的条件,并给出了MC局部谱子空间的一个刻画.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.111501419)the Doctoral Fund of Shaanxi province of China(Grant No.2017BSHEDZZ108)the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2021JM-519)。
文摘By the new spectrum originated from the single-valued extension property,we give the necessary and sufficient conditions for a bounded linear operator defined on a Banach space for which property(ω)holds.Meanwhile,the relationship between hypercyclic property(or supercyclic property)and property(ω)is discussed.
文摘设M_R=(T R O S)是定义在Banach空间X⊕Y上的2×2上三角算子矩阵,则T和S满足性质(gw)(或性质(gb))推不出M_R满足性质(gw)(或性质(gb)),即使R=0.文章主要利用局部谱理论的知识,研究了Banach空间上2×2上三角算子矩阵在什么情况下满足性质(gb)和性质(gw).
基金This work was supported in part by the National Natural Science Foundation of China （Grant No. 11171066）, the Natural Science Foundation of Fujian Province （Grant No. 2011J05002）, and the Specialized Research Fund for the Doctoral Program of Higher Education （Grant Nos. 2010350311001 and 20113503120003）.
文摘In this paper, we use the constancy of certain subspace valued mappings on the components of the generalized Kato resolvent set and the equivalences of the single-valued extension property at a point 0 for operators which admit a generalized Kato decomposition to obtain a classification of the components of the generalized Kato resolvent set of operators. We also give some applications of these results
文摘Let T be a Banach space operator, E（T） be the set of all isolated eigenvalues of T and π（T） be the set of all poles of T. In this work, we show that Browder＇s theorem for T is equivalent to the localized single-valued extension property at all complex numbers λ in the complement of the Weyl spectrum of T, and we give some characterization of Weyl＇s theorem for operator satisfying E（T） = π（T）. An application is also given.
文摘本文研究了Banach空间中上三角算子矩阵MC(A C 0 B)∈L(X■Y)的局部谱性质,其中A∈L(X),B∈L(Y),C∈L(Y,X),X,Y是无穷维复Banach空间,L(X,Y)表示X到Y的所有有界线性算子.首先考察了MC的单值扩张性,借助于向量值解析函数和解析核等工具给出了集合S(MC)={λ∈C:MC在λ没有单值扩张性}的刻画,并得到对任意C∈L(Y,X)等式S(MC)=S(A)∪S(B)都成立的条件.进一步,研究了MC的单值扩张性扰动,得到了对于给定A∈L(X),B∈L(Y),等式S(MC)=S(A)∪(B)成立时C所需的条件.同时,举例说明了这些条件的合理性.最后,把所得结果运用到上三角算子矩阵的谱和局部谱上,得到了σ(MC)=σ(A)∪σ(B)和σMMC(x■0)=σA(x)成立的条件,并给出了MC局部谱子空间的一个刻画.
