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1.
设T是复希尔伯特空间H上的有界线性算子,若对任意的x∈H,T满足||T~(k+2)x||||Tx||~k≥||T~2x||~(k+1),则称T为拟-k-仿正规算子,其中k为正整数.该文给出了拟-k-仿正规算子的一些性质,如拟-k-仿正规算子是极,作为此性质的应用,证明了拟-k-仿正规算子满足Weyl定理.  相似文献   

2.
利用一个不动点定理,研究一类具有p-laplace算子的二阶微分方程的两点边值问题(φp(x′(t)))′+q(t)f(t,x(t),x′(t))=0,x(0)-B(x′(0))=0,x(1)+B(x′(1))=0.给出了三个正解存在的充分条件.推广并丰富了以往文献的一些结论.  相似文献   

3.
陈为雄 《计算数学》1984,6(4):388-395
§1.前言 设X和Y是Banach空间,p(x)是定义在区域G X上并取值于Y的非线性算子。假定p(x)有Frechet导算子p’(x),为了近似解算子方程 p(x)=0, (1)研究了如下的迭代程序: x_(n 1)=x_n-A_np(x_n), A_(n 1)=2A_n-A_np(x_(n 1)A_n,(2)这里x_0∈G和A_0∈(Y→X)都是初始近似,其中x_0是方程(1)的近似解,而A_0则是p(x_0)的近似过算子。[1]在一些条件下证明了程序(2)收敛于方程(1)的解。  相似文献   

4.
本文用算子的最小模来估计伪条件数ω_i(A) (见[1][2])。主要结果是ω(A)≥‖A‖/γ(A) (i=1,2)和ω_i(A)=‖A‖/γ(A) (i=3,4)。由此得出判断的一个简单而有用的定理,它包含了[2]的结果。顺便也肯定地回答了[2]中所提出的问题。 在本文中X、Y是Banach空间,A∈[X,Y),A的最小模γ(A)=inf{‖Ax‖;p(x N(A))=1}。文中用到γ(A)的性质见[3.pp94—100] 定理Ⅰ 设A∈[X,Y],m(A) inf{‖Ax‖;‖x‖=1 l>0。那么ρ(A,M_0∩N_0)=  相似文献   

5.
Y.Yajima在[1]中研究了对两空间类K,k′,这里K′K,在什么条件下x∈I(K)蕴含x∈I(K′),在[1]的所有定理中,有两个定理是在正则性条件下给出的(定理3.1和定理3.3),本文指出这两个定理在非正则情况下仍然成立,且其它条件还可适当地减弱,另外还给出了一个类似的新结果。  相似文献   

6.
本文讨论非线性方程f(x,λ)=θ的分歧问题,这里f:x×R→Y为非线性可微映射, x,Y为Banaclh空间.利用偏导算子A=fx(x0,λ0)的广义逆A ,研究了一类由非单特征值引出的分歧问题,给出了刻划分歧性的定理,推广了Crandall M G与Robinowitz P H的由单特征值引出的分歧性定理.  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.
研究了有界线性算子的(h)性质和(gh)性质的问题.利用算子的单值扩张性的方法,获得了Banach空间上有界线性算子的(h)性质和(gh)性质的几个充分必要条件以及它们与其他Weyl型定理之间的关系,(h)性质和(gh)性质是a-Weyl定理和广义a-Weyl定理的推广.  相似文献   

9.
引进了相对弱$R$-子集和类($W$-)KKM$(X,Y,Z)$的概念,给出了相对KKM映射与相对弱$R$-子集之间的等价关系以及$W$-KKM$(X,Y,Z)$的一个性质,然后给出了两个连续选择定理并得到不动点定理和重合点定理, 最后,在一致拓扑空间上得到具有弱-KKM性质的映射的几乎不动点,不动点和重合点的存在定理.  相似文献   

10.
李江波 《数学杂志》1990,10(1):47-54
本文研究了两变量函数 f(x,y)用单变量函数 g(x)作混合范数逼近问题,即求g~*(x)∈G,G 是一 Haar 子空间,使(?)integral from Y|f(x,y)-g~*(x)|dμ=(?)integral from Y|f((?),y)-g(x)|dμ我们建立了包括交错定理、de la Vallee Poussin 定理、唯一性定理和强唯一性定理在内的 Chebyshev 逼近理论。  相似文献   

11.
按文[1]中方法得到几个对凝聚映象的不动点定理,还扩充文[2]中对于算子方程Ax B x=x到Ax B x Cx=x可解性的某些结论.主要结果是定理2、定理3与定理5.  相似文献   

12.
Hammerstein型非线性积分方程正解的个数   总被引:10,自引:6,他引:4  
郭大钧 《数学学报》1979,22(5):584-595
<正> 本文是作者工作[8]、[9]的继续.在[9]中作者利用Leray-Schauder拓扑度理论研究了多项式型Hammerstein非线性积分方程的固有值,即设  相似文献   

13.
The probabilistic machinery (Central Limit Theorem, Feynman-Kac formula and Girsanov Theorem) is used to study the homogenization property for PDE with second-order partial differential operator in divergence-form whose coefficients are stationary, ergodic random fields. Furthermore, we use the theory of Dirichlet forms, so that the only conditions required on the coefficients are non-degeneracy and boundedness. Received: 27 August 1999 / Revised version: 27 October 2000 / Published online: 26 April 2001  相似文献   

14.
Let X and Y be Banach spaces andtl (x, y). An operator T: X Y is called an RN-operator if it transforms every X-valued. measure ¯m of bounded variation into a Y-valued measure having a derivative with respect to the variation of the measure ¯m. The notions of T-dentability and Ts-dentability of bounded sets in Banach spaces are introduced and in their terms are given conditions equivalent to the condition that T is an RN-operator (Theorem 1). It is also proved that the adjoint operator is an RN-operator if and only if for every separable subspace Xo of X the set (T|Xo)*(Y*) is separable (Theorem 2).Translated from Matematicheskie Zametki, Vol. 22, No. 2, pp. 189–202, August, 1977.  相似文献   

15.
Herstein定理的推广   总被引:5,自引:0,他引:5  
1955年Herstein将著名的Jacobson定理推广为:定理A.如果对R中任意x,y,存在可依赖于x,y的整系数多项式p(t),使[x-x2p(x),y]=0,则R是交换的.本文利用多项式的系数和定义了n元多项式,f(x1,x2…,xn)的Fk性质,并以此证明了一个环的交换性定理,当n=1时,即得到定理A.  相似文献   

16.
Ruelle operator defined by weakly contractive iterated function systems (IFS) satisfying the open set condition was discussed in the paper [K.S. Lau, Y.L. Ye, Ruelle operator with nonexpansive IFS, Studia Math. 148 (2001) 143-169]. There, one of our theorems gave a sufficient condition for the possession of the Perron-Frobenius property. In this paper we consider Ruelle operator defined by nonexpansive IFS on the line instead of by weakly contractive one. And we prove, under the same condition, that the newly defined Ruelle operator has the Perron-Frobenius property. It extends the Ruelle-Perron-Frobenius theorem partially to the nonexpansive IFS.  相似文献   

17.
We consider the near-ring C(V) of all continuous operators on a locally convex space V. Like in the Theorem of Stone-Weierstrass the question arises which subnear-rings N have the property that every operator in C(V) can be approximated by elements of N on compact subsets of V. It is our aim to show that this can be achieved with certain primitive subnear-rings of C(V). For this we invoke a deep Theorem of Wielandt-Betsch on interpolation properties of primitive near-rings. We also stress the fact that such a Theorem of Stone-Weierstrass type can only be obtained in the context of near-rings.  相似文献   

18.
We generalize a Theorem of Koldunov [2] and prove that a disjointness proserving quasi-linear operator between Resz spaces has the Hammerstein property.  相似文献   

19.
集值度量广义逆的存在性   总被引:2,自引:2,他引:0  
设X,Y为Banach空间,T∈L(X,Y)为从X到Y的线性算子,D(T),N(T),R(T)分别为T的定义域,核空间与值域,使用算子T的自身性质,给出T具有集值度量广义逆T和R(T)D(T)的充分必要条件.  相似文献   

20.
Several upper bounds are known for the numbers of primitive solutions (x; y) of the Thue equation (1) j F(x; y) j = m and the more general Thue inequality (3) 0 &lt; j F(x; y) j m. A usual way to derive such an upper bound is to make a distinction between "small" and "large" solutions, according as max( j x j ; j y j ) is smaller or larger than an appropriate explicit constant Y depending on F and m; see e.g. [1], [11], [6] and [2]. As an improvement and generalization of some earlier results we give in Section 1 an upper bound of the form cn for the number of primitive solutions (x; y) of (3) with max( j x j ; j y j )Y0 , wherec 25 is a constant and n denotes the degree of the binary form F involved (cf. Theorem 1). It is important for applications that our lower bound Y0 for the large solutions is much smaller than those in [1], [11], [6] and [4], and is already close to the best possible in terms of m. ByusingTheorem1 we establish in Section 2 similar upper bounds for the total number of primitive solutions of (3), provided that the height or discriminant of F is suficiently large with respect to m (cf. Theorem 2 and its corollaries). These results assert in a quantitative form that, in a certain sense, almost all inequalities of the form (3) have only few primitive solutions. Theorem 2 and its consequences are considerable improvements of the results obtained in this direction in [3], [6], [13] and [4]. The proofs of Theorems 1 and 2 are given in Section 3. In the proofs we use among other things appropriate modifications and refenements of some arguments of [1] and [6].  相似文献   

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