共查询到17条相似文献,搜索用时 156 毫秒
1.
Let H1, H2 and H3 be infinite dimensional separable complex Hilbert spaces. We denote by M(D,E,F) a 3×3 upper triangular operator matrix acting on H1⊕H2⊕H3 of the form M(D,E,F)=(A D E 0 B F 0 0 C). For given A ∈ B(H1), B ∈ B(H2) and C ∈ B(H3), the sets UD,E,F σp(M(D,E,F)), ∪D,E,F σr(M(D,E,F)), ∪D,E,F σc(M(D,E,F)) and ∪D,E,F σ(M(D,E,F)) are characterized, where D ∈ B(H2,H1), E ∈ B(H3, H1), F ∈ B(H3, H2) and σ(·), σp(·), σr(·),σc(·) denote the spectrum, the point spectrum, the residual spectrum and the continuous spectrum, respectively. 相似文献
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《数学的实践与认识》2013,(16)
设H,K为可分Hilbert空间,A∈B(H),B∈B(H,K)和D∈B(K)是给定的有界线性算子,定义缺项算子矩阵N_C=(ABCD).得到存在C∈B(K,H)使得N_C是上半Fredholm算子(下半Fredholm算子,Fredholm算子)的条件. 相似文献
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Let H1, H2 and H3 be infinite dimensional separable complex Hilbert spaces. We denote by M(D,V,F) a 3×3 upper triangular operator matrix acting on Hi +H2+ H3 of theform M(D,E,F)=(A D F 0 B F 0 0 C).For given A ∈ B(H1), B ∈ B(H2) and C ∈ B(H3), the sets ∪D,E,F^σp(M(D,E,F)),∪D,E,F ^σr(M(D,E,F)),∪D,E,F ^σc(M(D,E,F)) and ∪D,E,F σ(M(D,E,F)) are characterized, where D ∈ B(H2,H1), E ∈B(H3, H1), F ∈ B(H3,H2) and σ(·), σp(·), σr(·), σc(·) denote the spectrum, the point spectrum, the residual spectrum and the continuous spectrum, respectively. 相似文献
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记■为Hilbert空间■上的上三角算子矩阵.我们借助对角元A,B和C的谱性质给出了σ_*(M_(D,E,F))=σ_*(A)∪σ_*(B)∪σ_*(C)对任意D∈B(H_2,H_1),E∈B(H_3,H_1),F∈B(H_3,H_2)均成立的充要条件,其中σ_*代表某类特定的谱,如点谱、剩余谱和连续谱等.此外,给出了一些例证. 相似文献
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《数学的实践与认识》2013,(19)
令H_1,H_2,H_3是可分的复Hilbert空间,记M=(AEF0BD00C)为H_1⊕H_2⊕H_3上的3×3上三角算子矩阵.设A∈B(H_1),B∈B(H_2),C∈B(H_3)是给定的算子,利用对角元算子A,B,C的值域和零空间性质描述了算子矩阵M值域R(M)的闭性. 相似文献
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A∈B(H)称为是一个Drazin可逆的算子,若A有有限的升标和降标.用σ_D(A)={λ∈C:A-λI不是Drazin可逆的)表示Drazin谱集.本文证明了对于Hilbert空间上的一个2×2上三角算子矩阵M_C=■,从σ_D(A)∪σ_D(G)到σ_D(M_C)的道路需要从前面子集中移动σ_D(A)∩σ_D(B)中一定的开子集,即有等式:σ_D(A)∪σ_D(B)=σ_D(M_C)∪G,其中G为σ_D(M_C)中一定空洞的并,并且为σ_D(A)∪σ_D(B)的子集.2×2算子矩阵不一定满足Weyl定理,利用Drazin谱,我们研究了2×2上三角算子矩阵的Weyl定理,Browder定理,a-Weyl定理和a-Browder定理. 相似文献
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Banach空间中算子的秩定理 总被引:2,自引:0,他引:2
设E和F是Banach空间,B(E,F)表示映E到F的有界线性算子全体.记T+0 ∈ B(F,E)为T0 ∈ B(E,F)的一个广义逆.本文证明,每一个具有‖T+0(T-T0)‖<1的算子T ∈ B(E,F),B≡(I+T+0(T-T0))-1T+0是T的广义逆当且仅当(I-T+0T0)N(T)=N(T0),其中N(·)表示括弧中算子的零空间.这一结果改进了Nashed和Cheng的一个有用的定理,并进一步证明Nashed和Cheng的一个引理对半-Fredholm算子有效但一般未必成立. 相似文献
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《数学的实践与认识》2017,(23)
令H为无限维且复可分的Hilbert空间,B(H)为H上的有界线性算子全体.若T∈B(H)满足σ_w(T)=σ_b(T),则称T有Browder定理,其中σ_ω(T)和σ_b(T)分别表示算子T的Weyl谱和Borwder谱;对任意的紧算子K∈B(H),若T+K有Browder定理,则称T满足Browder定理的稳定性.给出了2-阶上三角算子矩阵的平方满足Borwder定理的稳定性的充要条件. 相似文献
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基于值域的稠密性和闭性,有界线性算子的点谱可进一步细分为互不相交的四个组成部分,即四类点谱.设H_1,H_2,H_3为无穷维复可分Hilbert空间,记M_(D,E,F)=(A D E0 B F0 0 C)∈B(H_1H_2H_3).当对角算子A,B,C固定时,给出了M_(D,E,F)的四类点谱随D,E,F扰动的完全描述. 相似文献
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We call T ∈ B(H) consistent in Fredholm and index (briefly a CFI operator) if for each B ∈ B(H),T B and BT are Fredholm together and the same index of B,or not Fredholm together.Using a new spectrum defined in view of the CFI operator,we give the equivalence of Weyl’s theorem and property (ω) for T and its conjugate operator T* .In addition,the property (ω) for operator matrices is considered. 相似文献
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Rank theorems of operators between Banach spaces 总被引:13,自引:0,他引:13
MA Jipu 《中国科学A辑(英文版)》2000,43(1):1-5
Let E and F be Banach spaces, and B(E,F) all of bounded linear operators on E into F. Let T0∈B(E,F) with an outer inverse T#0∈B(F,E). Then a characteristic condition of S=(I+T#0(T-T0))-1T#0 with T∈B(E,F) and ‖T#0(T-T0)‖<1, being a generalized inverse of T, is presented, and hence, a rank theorem of operators on E into F is established (which generalizes the rank theorem of matrices to Banach spaces). Consequently, an improved finite rank theorem and a new rank theorem are deduced. These results will be very useful to nonlinear functional analysis. 相似文献
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若任给x∈H,‖Tx‖~2≤‖T~2x‖·‖x‖,T∈B(H)称为是一个paranormal算子.T∈B(H)称为代数paranormal算子,若存在非常值复值多项式p,使得p(T)为para- normal算子.本文利用代数paranormal算子的谱集的特点,研究了代数paranormal算子以及该算子的拟仿射变换的Weyl型定理. 相似文献
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刘明学 《应用泛函分析学报》2000,2(4):328-330
证明关于压缩算子的如下不变子空间定理:如果T是Hilbert空间H上的压缩算子,且集合Z’={λ∈D;存在z∈H,使得‖z‖=1,且‖(λ-T)z‖<1/3(1-‖λ‖}是开单位圆D的控制集,那么T有非平凡的不变子空间,这个定理包含了S.Brown,B.Chevreau,C.fPearcy和B.Beauzamy的两个重要结果作为特殊情况,特别是,为个定理包含了S.Brown等人的Hilbert空间上的每个具有厚谱的压缩算子都有平凡的不变子空间这个重要结果作为特殊情况。 相似文献
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Xiao Hong CAO Mao Zheng GUO Bin MENG 《数学学报(英文版)》2006,22(1):169-178
When A ∈ B(H) and B ∈ B(K) are given, we denote by Mc an operator acting on the Hilbert space HΘ K of the form Me = ( A0 CB). In this paper, first we give the necessary and sufficient condition for Mc to be an upper semi-Fredholm (lower semi-Fredholm, or Fredholm) operator for some C ∈B(K,H). In addition, let σSF+(A) = {λ ∈ C : A-λI is not an upper semi-Fredholm operator} bc the upper semi-Fredholm spectrum of A ∈ B(H) and let σrsF- (A) = {λ∈ C : A-λI is not a lower semi-Fredholm operator} be the lower semi Fredholm spectrum of A. We show that the passage from σSF±(A) U σSF±(B) to σSF±(Mc) is accomplished by removing certain open subsets of σSF-(A) ∩σSF+ (B) from the former, that is, there is an equality σSF±(A) ∪σSF± (B) = σSF± (Mc) ∪& where L is the union of certain of the holes in σSF±(Mc) which ilappen to be subsets of σSF- (A) A σSF+ (B). Weyl's theorem and Browder's theorem are liable to fail for 2 × 2 operator matrices. In this paper, we also explore how Weyl's theorem, Browder's theorem, a-Weyl's theorem and a-Browder's theorem survive for 2 × 2 upper triangular operator matrices on the Hilbert space. 相似文献