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缺项算子矩阵的二阶代数(Ⅰ) 总被引:1,自引:0,他引:1
对于任意给定的二阶多项式p(t);本文获得希尔伯特空间上形如(?)的缺项算子矩阵具有一个补T使得p(T)=0成立的充分必要条件以及使得p(T)=0且p(T)的范数不大于事先给定常数的充分必要条件.进而还求出所有可能的二阶代数补,特别地,对有限维情形给出简洁的表示。 相似文献
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研究二阶算子矩阵代数中的全可导点.利用线性映射与算子矩阵代数运算,以及套代数理论的相关结果,给出并证明了第二行第二列元素为可逆算子,其余元素为零算子的二阶矩阵是二阶算子矩阵代数的关于强算子拓扑的全可导点,推广了相关文献中的结果. 相似文献
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研究二阶算子矩阵代数中的全可导点.利用线性映射于算子矩阵代数运算,以及套代数理论的相关结果.给出并证明了E=[■](V是可逆算子)是二阶算子矩阵代数的关于强算子拓扑的全可导点,推广了相关文献的结果. 相似文献
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有界线性算子的点谱和剩余谱分别可进-步细分为两类:σ_(p1),σ_(p2)和σ_(r1),σ_(r2).设H,K为无穷维可分的Hilbert空间,本文将对于给定的A ∈B (H),B ∈B(K),给出了缺项算子M_C=(AC/OB)关于分类后所得四种谱的扰动结果. 相似文献
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Let =(A C X B)be a 2×2 operator matrix acting on the Hilbert space н( )κ.For given A ∈B (H),B ∈B(K)and C ∈B(K,H)the set Ux∈B(H,к)σe(Mx)is determined,where σe(T)denotes the essential spectrum. 相似文献
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一类缺项算子矩阵的谱补问题 总被引:8,自引:0,他引:8
对于Hilbert空间上的2×2算子矩阵,其中A∈B(H),C∈B(K,H),D∈B(H,K)给定,当X取遍B(K)中算子时,我们给出所有Nx的谱之交集和并集的刻画. 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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In this paper we consider various aspects of generalized invertibility of the operator matrix acting on a Banach space X⊕Y. 相似文献
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Weyl spectra of operator matrices 总被引:1,自引:0,他引:1
Woo Young Lee 《Proceedings of the American Mathematical Society》2001,129(1):131-138
In this paper it is shown that if is a upper triangular operator matrix acting on the Hilbert space and if denotes the ``Weyl spectrum", then the passage from to is accomplished by removing certain open subsets of from the former, that is, there is equality where is the union of certain of the holes in which happen to be subsets of .
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Invertible completions of operator matrices 总被引:8,自引:0,他引:8
Katsutoshi Takahashi 《Integral Equations and Operator Theory》1995,21(3):355-361
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Given a pair of matrices (AB) it is well known that its invariant factors and its controllability indices form a complete set of invariants for the Γ-equivalence [11] or block similarity [5]. How do they vary by adding columns to B? This problem was solved in [12] when B = 0; here we give a complete answer for this question. 相似文献
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Weyl's theorem for operator matrices 总被引:11,自引:0,他引:11
Woo Young Lee 《Integral Equations and Operator Theory》1998,32(3):319-331
Weyl's theorem holds for an operator when the complement in the spectrum of the Weyl spectrum coincides with the isolated points of the spectrum which are eigenvalues of finite multiplicity. By comparison Browder's theorem holds for an operator when the complement in the spectrum of the Weyl spectrum coincides with Riesz points. Weyl's theorem and Browder's theorem are liable to fail for 2×2 operator matrices. In this paper we explore how Weyl's theorem and Browder's theorem survive for 2×2 operator matrices on the Hilbert space.Supported in part by BSRI-97-1420 and KOSEF 94-0701-02-01-3. 相似文献
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In this paper we consider certain matrix equations in the field of Mikusiński operators, and construct a method for obtaining an approximate solution which allows working with numerical constants instead of operators. The theory of diagonally dominant matrices is applied for the analysis, existence and character of the obtained solutions. We introduce a method for determining approximate solutions of a discrete analogue for operational differential equations and give conditions for their existence. The error of the approximation is estimated. 相似文献
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Let f be a function from \({\mathbb{R}_{+}}\) into itself. A classic theorem of K. Löwner says that f is operator monotone if and only if all matrices of the form \({\left [\frac{f(p_i) - f(p_j)}{p_i-p_j}\right ]_{\vphantom {X_{X_1}}}}\) are positive semidefinite. We show that f is operator convex if and only if all such matrices are conditionally negative definite and that f (t) = t g(t) for some operator convex function g if and only if these matrices are conditionally positive definite. Elementary proofs are given for the most interesting special cases f (t) = t r , and f (t) = t log t. Several consequences are derived. 相似文献
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Spectra of upper triangular operator matrices 总被引:4,自引:0,他引:4
C. Benhida E. H. Zerouali H. Zguitti 《Proceedings of the American Mathematical Society》2005,133(10):3013-3020
Let be given Banach spaces. For and , let be the operator defined on by . We give sufficient conditions on to get where runs over a large class of spectra. We also discuss the case of some spectra for which the latter equality fails.