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1.
设MG=[ O B^A C]是从Hilbert空间H+K到H+K中的2×2上三角算子矩阵.该文主要研究MC的Drazin可逆性和Mc的Drazin谱.此外,对给定算子A∈B(H)和B∈B(K),将给出在一定条件下所有上三角算子矩阵Mc的Drazin谱的交∩C∈B(K,H)σD(Mc)的具体表达式。  相似文献   

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2×2阶上三角算子矩阵的谱扰动   总被引:2,自引:1,他引:1  
研究了Hilbert空间H⊕K上的2×2阶上三角算子矩阵MC=(A O C B)当A,B给定,C为任意有界线性算子时,对MC的点谱、剩余谱、连续谱的扰动分别给出了描述.  相似文献   

3.
2×2 上三角算子矩阵的 Drazin 谱   总被引:1,自引:0,他引:1       下载免费PDF全文
设MC= [ AC ; 0 B ]是从Hilbert空间H K 到HK 中的 2×2 上三角算子矩阵. 该文主要研究 MC的Drazin可逆性和MC 的 Drazin谱.此外, 对给定算子A∈B}(H) 和 B∈B}(K), 将给出在一定条件下所有上三角算子矩阵MC的Drazin谱的交∩σD (MC) 的具体表达式.  相似文献   

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设H和K是复无穷维可分Hilbert空间,A∈B(H),B∈B(K),C∈B(K,H)且M_C=(ACOB).本文给出了上三角算子矩阵M_C的Weyl谱、本性谱、谱、左谱、右谱、下半本性谱、下半Weyl谱和上半Weyl谱的Fredholm扰动的完全刻画.  相似文献   

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Drazin谱和算子矩阵的Weyl定理   总被引:2,自引:0,他引:2       下载免费PDF全文
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   

6.
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   

7.
本文研究了Banach空间中上三角算子矩阵■∈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)∪S(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σMC(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.  相似文献   

8.
设M_C表示Hilbert空间H_1⊕H_2上的上三角算子矩阵M_C=(ACOB),用∩_*表示∩_(C∈B(H_2,H_1))σ_*(M_C),其中*表示某类谱,称满足等式∩_*=σ_*(M_0)的谱为固零谱,本文集中给出上三角算子矩阵的三类固零谱,并举例说明谱等式σ_*(M_0)=σ_*(A)∪σ_*(B)对这三类固零谱失效.  相似文献   

9.
Let A ∈ B(X) and B ∈ B(Y), MC be an operator on Banach space X ⊕ Y given A C by MC =A generalized Drazin spectrum defined by σgD(T) = {λ∈ C : T-0 BλI is not generalized Drazin invertible} is considered in this paperIt is shown thatσgD(A) ∪σgD(B) = σgD(MC) ∪ WgD(A, B, C),where WgD(A, B, C) is a subset of σgD(A) ∩σgD(B) and a union of certain holes in σgD(MC).Furthermore, several sufficient conditions for σgD(A) ∪σgD(B) = σgD(MC) holds for every C ∈ B(Y, X) are given.  相似文献   

10.
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   

11.
Using rank-1 reduction formula and the vector space spanned by the real rank-1 matrices, we present a different way to show that the maximum possible rank of the 2?×?2?×?2 tensors over the real field is 3. Following, we obtain that the maximum rank of the 2?×?2?×?2?×?2 tensors over the real field is less than or equal to 5 and propose another way to show that the maximum rank of the 2?×?2?×?2?×?2 tensors over the complex field is 4, except one special case.  相似文献   

12.
We study the strength of some combinatorial principles weaker than Ramsey theorem for pairs over RCA0. First, we prove that Rainbow Ramsey theorem for pairs does not imply Thin Set theorem for pairs. Furthermore, we get some other related results on reverse mathematics using the same method. For instance, Rainbow Ramsey theorem for pairs is strictly weaker than ErdSs- Moser theorem under RCA0.  相似文献   

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As a first step in the classification of nonsingular 2×2×2×2 hypercubes up to equivalence, we resolve the case where the base field is finite and the hypercubes can be written as a product of two 2×2×2 hypercubes. (Nonsingular hypercubes were introduced by D. Knuth in the context of semifields. Where semifields are related to hypercubes of dimension 3, this paper considers the next case, i.e., hypercubes of dimension 4.) We define the notion of ij-rank (with 1 ≤ i < j ≤ 4) and prove that a hypercube is the product of two 2×2×2 hypercubes if and only if its 12-rank is at most 2. We derive a ‘standard form’ for nonsingular 2×2×2×2 hypercubes of 12-rank less than 4 as a first step in the classification of such hypercubes up to equivalence. Our main result states that the equivalence class of a nonsingular 2×2×2×2 hypercube M of 12-rank 2 depends only on the value of an invariant δ 0(M) which derives in a natural way from the Cayley hyperdeterminant det0 M and another polynomial invariant det M of degree 4. As a corollary we prove that the number of equivalence classes is (q + 1)/2 or q/2 depending on whether the order q of the field is odd or even.  相似文献   

16.
The infra-red spectra of two polyhalogenated ethanes, 1, 1-difluoro-2, 2-dichloro ethane and 1, 2-dibromo-1, 1, 2, 2-tetrachloro ethane were obtained in the region of 2·5–38 microns. The spectra of CHF2-CHCl2 were obtained in gas, liquid and solid states and also in solvents of widely varying dielectric constants. These spectral studies showed that the molecule exists in the form of two rotational isomers. The fundamental modes of the two isomers were identified on the basis of intensity changes from gas to liquid to solid and in solvents of different dielectric constants. The observed infra-red absorption bands have been assigned in terms of the fundamental absorption bands. Spectra of CBrCl2-CBrCl2 were obtained in the solid and vapour phase and in various solvents. These spectra showed that CBrCl2-CBrCl2 exists only in the trans form. The infra-red spectra, combined with Raman data available from literature was used for complete assignment of the observed absorption bands.  相似文献   

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A short Matlab implementation realizes a flexible isoparametric finite element method up to quadratic order for the approximation of elliptic problems in two-dimensional domains with curved boundaries. Triangles and quadrilaterals equipped with varying quadrature rules allow for mesh refinement. Numerical examples for the Laplace equation with mixed boundary conditions indicate the flexibility of isoparametric finite elements.  相似文献   

20.
Necessary conditions are obtained for the existence of a 2 – (v, k, ) design, for which the block intersection sizess 1,s 2, ...,s n satisfys 1 s 2 ... s n s (mod 2 e ), wheree is odd. These conditions are obtained by combining restrictions on the Smith Normal Form of the incidence matrix of the design with some well known properties of self-orthogonal binary codes with all weights divisible by 4.Research done at AT&T Bell Laboratories.  相似文献   

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