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1.
In this paper,continuous homogeneous selections for the set-valued metric generalized inverses T of linear operators T in Banach spaces are investigated by means of the methods of geometry of Banach spaces.Necessary and sufficient conditions for bounded linear operators T to have continuous homogeneous selections for the set-valued metric generalized inverses T are given.The results are an answer to the problem posed by Nashed and Votruba.  相似文献   

2.
《分析论及其应用》2012,28(2):146-155
Utilizing the stability characterizations of generalized inverses of linear operator, we investigate the existence of generalized resolvent of linear pencils in Banach spaces. Some practical criterions for the existence of generalized resolvents of the linear pencil λ→ T λ S are provided and an explicit expression of the generalized resolvent is also given. As applications, the characterization for the Moore-Penrose inverse of the linear pencil to be its generalized resolvent and the existence of the generalized resolvents of linear pencils of finite rank operators, Fredholm operators and semi-Fredholm operators are also considered. The results obtained in this paper extend and improve many results in this area.  相似文献   

3.
METRIC GENERALIZED INVERSE OF LINEAR OPERATOR IN BANACH SPACE***   总被引:13,自引:0,他引:13  
The Moore-Penrose metric generalized inverse T of linear operator T in Banach space is systematically investigated in this paper. Unlike the case in Hilbert space, even T is a linear operator in Banach Space, the Moore-Penrose metric generalized inverse T is usually homogeneous and nonlinear in general. By means of the methods of geometry of Banach Space, the necessary and sufficient conditions for existence, continuitv, linearity and minimum property of the Moore-Penrose metric generalized inverse T will be given, and some properties of T will be investigated in this paper.  相似文献   

4.
. IntroductionIn this paper we adopt the same notations on generalized inverses of matrices andprojectors as those in [1].Several rePresentations for the generalized inverses of matrices, for example, those forthe Moors-Penrose inverse A and the Drazin inverse A(d), have led to[1--4]:where k = index (A).In order to study the matrix form of the above-mentioned operator represelltations,we denote linear operators by A, B,' ', and their matrices by the corresponding A, B,' '.All of the li…  相似文献   

5.
Let X, Y be Banach spaces and M be a linear subspace in X × Y = {{x, y}|x ∈ X, y ∈ Y }. We may view M as a multi-valued linear operator from X to Y by taking M (x) = {y|{x, y} ∈ M }. In this paper, we give several criteria for a single-valued operator from Y to X to be the metric generalized inverse of the multi-valued linear operator M . The principal tool in this paper is also the generalized orthogonal decomposition theorem in Banach spaces.  相似文献   

6.
王月山  王学敏 《数学季刊》2006,21(2):288-292
The generalized Morrey spaces are introduced under the hypothesis that Rn is endowed with the general parabolic metric , and the boundedness properties are established in generalized Morrey spaces for a class of singular integral operators, which include Calderon-Zygmund singular integrals and their commutators with BMO.  相似文献   

7.
First we prove that the approximative compactness of a nonempty set C in a normed linear space can be reformulated equivalently in another way.It is known that if C is a semi-Chebyshev closed and approximately compact set in a Banach space X,then the metric projectorπC from X onto C is continuous.Under the assumption that X is midpoint locally uniformly rotund,we prove that the approximative compactness of C is also necessary for the continuity of the projectorπC by the method of geometry of Banach spaces.Using this general result we find some necessary and sufficient conditions for T to have a continuous Moore-Penrose metric generalized inverse T~ ,where T is a bounded linear operator from an approximative compact and a rotund Banach space X into a midpoint locally uniformly rotund Banach space Y.  相似文献   

8.
We give the necessary and sufficient condition for a bounded linear operator with property (ω) by means of the induced spectrum of topological uniform descent, and investigate the permanence of property (ω) under some commuting perturbations by power finite rank operators. In addition, the theory is exemplified in the case of algebraically paranormal operators.  相似文献   

9.
As a generalization of the Bernstein-Durrmeyer operators defined on the simplex, a class of general Bernstein-Durrmeyer operators is introduced. With the weighted moduli of smoothness as a metric, we prove a strong direct theorem and an inverse theorem of weak type for these operators by using a decomposition way. From the theorems the characterization of L^p approximation behavior is derived  相似文献   

10.
The generalized summation integral type operators with Beta basis functions are widely studied. At present, the investigations for the properties of these operators are only limited to the functions of bounded variation. Some authors studied the rate of point-wise rate of convergence, asymptotic formula of Voronovskaja type, and some direct results about these type of operators. The present paper considers the direct, inverse and equivalence theorems of modified summation integral type operators in the Lp spaces.  相似文献   

11.
In this paper,we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is "the generalized Neumann lemma" which is quite different from the method in [12] where "the generalized Banach lemma" was used. By the method of the perturbation analysis of bounded linear operators,we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces.  相似文献   

12.
The problems of perturbation and expression for the generalized inverses of closed linear operators in Banach spaces and for the Moore-Penrose inverses of closed linear operators in Hilbert spaces are studied. We first provide some stability characterizations of generalized inverses of closed linear operators under T-bounded perturbation in Banach spaces, which are exactly equivalent to that the generalized inverse of the perturbed operator has the simplest expression T+(I+δTT+)-1. Utilizing these results, we investigate the expression for the Moore-Penrose inverse of the perturbed operator in Hilbert spaces and provide a unified approach to deal with the range preserving or null space preserving perturbation. An explicit representation for the Moore-Penrose inverse of the perturbation is also given. Moreover, we give an equivalent condition for the Moore-Penrose inverse to have the simplest expression T(I+δTT)-1. The results obtained in this paper extend and improve many recent results in this area.  相似文献   

13.
Banach空间中线性算子的齐性广义逆   总被引:9,自引:0,他引:9  
王玉文  李双臻 《数学学报》2005,48(2):251-258
本文首先在Banach空间内引进拟线性投影算子的概念,由此给出Banach空 间内线性算子的齐性广义逆的统一定义。齐性广义逆包含线性广义逆、单值度量广义 逆.本文证得齐性广义逆存在的充分必要条件.  相似文献   

14.
We investigate the metric generalized inverses of linear operators in Banach spaces and their homogeneous selections, which was the research suggestion given by Nashed and Votruba (Bull. Am. Math. Soc. 80:831–835, 1974). We construct a kind of the bounded homoneneous selections for the set-valued metric generalized inverse. Criteria for the metric generalized inverses of linear operators and their homogeneous selections are given in terms of Moore–Penrose conditions. The research was supported in part by the National Science Foundation Grant (10671049) and the Science Foundation Grant of Heilongjiang Province.  相似文献   

15.
Universal Iterative Methods for Computing Generalized Inverses   总被引:2,自引:0,他引:2  
In this paper we construct a few iterative processes for computing {1,2} inverses of a linear bounded operator, based on the hyper-power iterative method or the Neumann-type expansion. Under suitable conditions these methods converge to the {1,2,3} or {1,2,4} inverses. Also, we specify conditions when the iterative processes converge to the Moore-Penrose inverse, the weighted Moore-Penrose inverse or to the group inverse. A few error estimates are derived. The advantages of the introduced methods over Tanabe's method [16] for computing reflexive generalized inverses are also investigated.  相似文献   

16.
讨论布尔矩阵的广义Moore-Penrose逆.给出了一些广义Moore-Penrose逆存在的充要条件以及广义Moore-Penrose逆的一些刻划.  相似文献   

17.
In this paper, we investigate the perturbation problem for the Moore–Penrose bounded quasi-linear projection generalized inverses of a closed linear operaters in Banach space. By the method of the perturbation analysis of bounded quasi-linear operators, we obtain an explicit perturbation theorem and error estimates for the Moore–Penrose bounded quasi-linear generalized inverse of closed linear operator under the T-bounded perturbation, which not only extend some known results on the perturbation of the oblique projection generalized inverse of closed linear operators, but also extend some known results on the perturbation of the Moore–Penrose metric generalized inverse of bounded linear operators in Banach spaces.  相似文献   

18.
王紫  王玉文 《数学学报》2018,61(5):751-760
本文给出Banach空间中闭线性算子的Moore-Penrose有界拟线性投影广义逆的一种新的扰动分析方法.运用的核心工具是广义Neumann引理,这与以往其他结果中所运用的广义Banach引理的处理方法极为不同,得到了闭线性算子的MoorePenrose有界拟线性广义逆的又一个扰动定理及三个误差界不等式.  相似文献   

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