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算子方程的解及算子张量积 总被引:1,自引:0,他引:1
本文讨论Hilbert空间上一类三阶二元算子方程组A*AC = αA*A2 + βAA*A;AA*C = λA*A2 + γAA*A,给出所有重交换的解(A,C).作为应用,得到算子张量积A(?)B+C(?)D和A1(?)A2(?)…(?)An为拟正规算子的充分必要条件. 相似文献
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本文讨论了算子A∈B(H)N为算子T∈B(H)的算子点谱的判定条件,特别得到:当T为亚正常算子时,A为T的算子点谱的判定条件,另外还得到kerτnT,A=kerτT,A成立的充分条件 相似文献
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本文用算子函数论的方法,研究了解析算子函数的Banach空间X,X0上的复合算子.给出此复合算子为有界的条件,并刻划了此复合算子在X0上为紧的特征. 相似文献
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本文考虑的算子,包括极大算子、分数次积分、poisson 算子,都是把 R~n 上的函数映到 R_ ~(n 1)上的函数的。主要结果有二个方面:首先解决了一个 Muckenhoupt 型问题,即,给出了 R 上的权函数ω(x)的充要条件,使得这些算子是从 L~p(R~n,ω(x))到某个加权 L~q(R_ ~(n 1))空间的有界算子;其次,建立了这些算子的一个因子分解。 相似文献
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西方给出了C^n中单位球上的带权的Bergman空间上具一般符号的Toeplitz算子和Hankel算子为紧的充要条件。 相似文献
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设p≥1,且A、B是Hilbert空间上两个正算子,T.Furuta给出若A≥B>0,那么对任意t∈[0,1]有,G(r,s)=A-r/2{Ar/2(A-t/2BpA-t/2)sAr/2}1-t+r/(p-t)+srA-r/2是关于r,s在r≥t及s≥1上单调递减的,我们给出该结果可以推广到多个算子的情形. 相似文献
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本文给出了Hamilton算子和Laplace算子间的一个积分公式,并指出文献[1]中的一个错误. 相似文献
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For a quiver Q, a k-algebra A, and an additive full subcategory 𝒳 of A-mod, the monomorphism category Mon(Q, 𝒳) is introduced. The main result says that if T is an A-module such that there is an exact sequence 0 → T m → … → T 0 → D(A A ) → 0 with each T i ∈ add(T), then Mon(Q, ⊥ T) =⊥(kQ ? k T); and if T is cotilting, then kQ ? k T is a unique cotilting Λ-module, up to multiplicities of indecomposable direct summands, such that Mon(Q, ⊥ T) =⊥(kQ ? k T). As applications, the category of the Gorenstein-projective (kQ ? k A)-modules is characterized as Mon(Q, 𝒢𝒫(A)) if A is Gorenstein; the contravariantly finiteness of Mon(Q, 𝒳) can be described; and a sufficient and necessary condition for Mon(Q, A) being of finite type is given. 相似文献
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Chunlan Jiang Shunhua Sun Zongyao Wang 《Transactions of the American Mathematical Society》1997,349(1):217-233
It is shown that given an essentially normal operator with connected spectrum, there exists a compact operator such that is strongly irreducible.
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Let K be an absolutely convex infinite-dimensional compact in a Banach space χ. The set of all bounded linear operators T on χ satisfying TK ⊃ K is denoted by G(K). Our starting point is the study of the closure WG(K) of G(K) in the weak operator topology. We prove that WG(K) contains the algebra of all operators leaving [`(lin(K))]\overline{{\rm lin}(K)} invariant. More precise results are obtained in terms of the Kolmogorov n-widths of the compact K. The obtained results are used in the study of operator ranges and operator equations. 相似文献
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Delio Mugnolo 《Integral Equations and Operator Theory》2006,54(3):441-464
We introduce an abstract setting that allows to discuss wave equations with time-dependent boundary conditions by means of
operator matrices. We show that such problems are well-posed if and only if certain perturbations of the same problems with
homogeneous, time-independent boundary conditions are well-posed. As applications we discuss two wave equations in Lp(0, 1) and in L2(Ω) equipped with dynamical and acoustic-like boundary conditions, respectively. 相似文献
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Karl Gustafson 《Linear and Multilinear Algebra》2013,61(1-3):139-159
The purpose of the present paper is to survey, from a historical perspective and including some new results, a theory which I will call operator trigonometry. This theory, which is little known, is closely associated with the numerical range W(A) of an operator A. Among the new results is a beautiful connection to numerical linear algebra, in which gradient descent and conjugate gradient convergence rates are shown to be trigonometric. 相似文献
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Karl Gustafson 《Linear and Multilinear Algebra》1994,37(1):139-159
The purpose of the present paper is to survey, from a historical perspective and including some new results, a theory which I will call operator trigonometry. This theory, which is little known, is closely associated with the numerical range W(A) of an operator A. Among the new results is a beautiful connection to numerical linear algebra, in which gradient descent and conjugate gradient convergence rates are shown to be trigonometric. 相似文献
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Lai Chunhui 《东北数学》1994,(3)
Quasi-range-preservingOperatorLaiChunhui(赖春晖)(DepartmentofMathematics,ZhangzhouTeachers,College,ZhangzhouFujian,363000)Abstra... 相似文献