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＂...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 perturba- tion 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.展开更多
We discuss the incomplete semi-iterative method (ISIM) for an approximate solution of a linear fixed point equations x=Tx+c with a bounded linear operator T acting on a complex Banach space X such that its resolvent h...We discuss the incomplete semi-iterative method (ISIM) for an approximate solution of a linear fixed point equations x=Tx+c with a bounded linear operator T acting on a complex Banach space X such that its resolvent has a pole of order k at the point 1. Sufficient conditions for the convergence of ISIM to a solution of x=Tx+c, where c belongs to the range space of R(I-T) k, are established. We show that the ISIM has an attractive feature that it is usually convergent even when the spectral radius of the operator T is greater than 1 and Ind 1T≥1. Applications in finite Markov chain is considered and illustrative examples are reported, showing the convergence rate of the ISIM is very high.展开更多
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 analysi...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.展开更多
Let X, Y be Banach spaces and M be a linear subspace in X x Y = {{x,y}lx E X,y C Y}. We may view M as a multi-valued linear operator from X to Y by taking M（x） = {yl（x,y} C M}. In this paper, we give several criter...Let X, Y be Banach spaces and M be a linear subspace in X x Y = {{x,y}lx E X,y C Y}. We may view M as a multi-valued linear operator from X to Y by taking M（x） = {yl（x,y} C 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.展开更多
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 Moo...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.展开更多
Let f be a C^1 map between two Banach spaces E and F. It has been proved that the concept of generalized regular points of f, which is a generalization of the notion of regular points of f, has some crucial applicatio...Let f be a C^1 map between two Banach spaces E and F. It has been proved that the concept of generalized regular points of f, which is a generalization of the notion of regular points of f, has some crucial applications in nonlinearity and global analysis. We characterize the generalized regular points of f using the three integer-valued （or infinite） indices M（x0）, Mc（x0） and Mr（x0） at x0 ∈ E generated by f and by analyzing generalized inverses of bounded linear operators on Banach spaces, that is, iff ＇（x0） has a generalized inverse in the Banach space B（E, F） of all bounded linear operators on E into F and at least one of the indices M（x0）, Mc（x0） and Mr（x0） is finite, then xo is a generalized regular point off if and only if the multi-index （M（x）, Me（x）, Mr（x）） is continuous at X0.展开更多
Stability and global error bounds are studied for a class of stepsize-dependent linear multistep methods for nonlinear evolution equations governed by ω-dissipative vector fields in Banach space.To break through the ...Stability and global error bounds are studied for a class of stepsize-dependent linear multistep methods for nonlinear evolution equations governed by ω-dissipative vector fields in Banach space.To break through the order barrier p≤1 of unconditionally contractive linear multistep methods for dissipative systems,strongly dissipative systems are introduced.By employing the error growth function of the methods,new contractivity and convergence results of stepsize-dependent linear multistep methods on infinite integration intervals are provided for strictly dissipative systems(ω<0)and strongly dissipative systems.Some applications of the main results to several linear multistep methods,including the trapezoidal rule,are supplied.The theoretical results are also illustrated by a set of numerical experiments.展开更多
By the method of geometry of Banach spaces, we have proven that a bounded linear operatorin Banach space is a compact linear one iff it can be uniformly approximated by a sequence of the finite rankbounded homogeneous...By the method of geometry of Banach spaces, we have proven that a bounded linear operatorin Banach space is a compact linear one iff it can be uniformly approximated by a sequence of the finite rankbounded homogeneous operators, which reveals the essence of the counter example given by Enflo.展开更多
Banach空间中线性算子分块矩阵的广义Drazin逆不仅在矩阵理论中有着重要应用,而且在控制论、系统论和微分方程等方面也有着重要应用.因此,给出了线性算子分块矩阵x=(a bc d)∈A(其中A为B代数)的广义舒尔补s=d-ca^db是广义Drazin逆条件...Banach空间中线性算子分块矩阵的广义Drazin逆不仅在矩阵理论中有着重要应用,而且在控制论、系统论和微分方程等方面也有着重要应用.因此,给出了线性算子分块矩阵x=(a bc d)∈A(其中A为B代数)的广义舒尔补s=d-ca^db是广义Drazin逆条件下此分块矩阵的广义Drazin逆的几种新特性,这些特性是广义舒尔补Drazin逆、广义舒尔补群逆和广义舒尔补为零情形下的推广形式.展开更多
文章主要研究Banach代数上两个元素和的伪Drazin逆的存在性.通过Pierce分解,得到两个元素和具有伪Drazin逆的一些条件.然后,研究了Banach代数上反三角算子矩阵的伪Drazin逆的存在性,证明了反三角算子矩阵(1 b 10)∈M_(2)(A)^(■),b∈(A...文章主要研究Banach代数上两个元素和的伪Drazin逆的存在性.通过Pierce分解,得到两个元素和具有伪Drazin逆的一些条件.然后,研究了Banach代数上反三角算子矩阵的伪Drazin逆的存在性,证明了反三角算子矩阵(1 b 10)∈M_(2)(A)^(■),b∈(A)^(■) 当且仅当b∈A^(■).最后,给出相应的数值例子来论证得到的结果.展开更多
基金Supported by the Nature Science Foundation of China(11471091 and 11401143)
文摘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 perturba- tion 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.
基金Project1 990 1 0 0 6 supported by National Natural Science Foundation of China,Doctoral Foundation of China,Chi-na Scholarship council and Laboratory of Computational Physics in Beijing of Chinathe second author is also supportedby the State Major Key
文摘We discuss the incomplete semi-iterative method (ISIM) for an approximate solution of a linear fixed point equations x=Tx+c with a bounded linear operator T acting on a complex Banach space X such that its resolvent has a pole of order k at the point 1. Sufficient conditions for the convergence of ISIM to a solution of x=Tx+c, where c belongs to the range space of R(I-T) k, are established. We show that the ISIM has an attractive feature that it is usually convergent even when the spectral radius of the operator T is greater than 1 and Ind 1T≥1. Applications in finite Markov chain is considered and illustrative examples are reported, showing the convergence rate of the ISIM is very high.
基金The questions were posed during B. de Pagter was visiting the Queen's University of Belfast in Spring 1997, whilst the second author stayed at Belfast
文摘In this paper we present some characterizations of Banach function spaces on which every continuous linear operator is regular.
基金Supported by National Nature Science Foundation of China(Grant No.11471091)
文摘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.
基金Supported by National Natural Science Foundation of China (Grant No. 11071051)
文摘Let X, Y be Banach spaces and M be a linear subspace in X x Y = {{x,y}lx E X,y C Y}. We may view M as a multi-valued linear operator from X to Y by taking M（x） = {yl（x,y} C 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.
基金the National Natural Science Foundation of China(No.19971023)the Heilongjiang Provincial Natural Science Foundation of China.
文摘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.
基金The National Natural Science Foundation of China(No10271053)the Foundation of Nanjing University of Finance andEconomics (NoB0556)
文摘Let f be a C^1 map between two Banach spaces E and F. It has been proved that the concept of generalized regular points of f, which is a generalization of the notion of regular points of f, has some crucial applications in nonlinearity and global analysis. We characterize the generalized regular points of f using the three integer-valued （or infinite） indices M（x0）, Mc（x0） and Mr（x0） at x0 ∈ E generated by f and by analyzing generalized inverses of bounded linear operators on Banach spaces, that is, iff ＇（x0） has a generalized inverse in the Banach space B（E, F） of all bounded linear operators on E into F and at least one of the indices M（x0）, Mc（x0） and Mr（x0） is finite, then xo is a generalized regular point off if and only if the multi-index （M（x）, Me（x）, Mr（x）） is continuous at X0.
基金supported by the Natural Science Foundation of China(Grant Nos.12271367,11771060)by the Science and Technology Innovation Plan of Shanghai,China(Grant No.20JC1414200)sponsored by the Natural Science Foundation of Shanghai,China(Grant No.20ZR1441200).
文摘Stability and global error bounds are studied for a class of stepsize-dependent linear multistep methods for nonlinear evolution equations governed by ω-dissipative vector fields in Banach space.To break through the order barrier p≤1 of unconditionally contractive linear multistep methods for dissipative systems,strongly dissipative systems are introduced.By employing the error growth function of the methods,new contractivity and convergence results of stepsize-dependent linear multistep methods on infinite integration intervals are provided for strictly dissipative systems(ω<0)and strongly dissipative systems.Some applications of the main results to several linear multistep methods,including the trapezoidal rule,are supplied.The theoretical results are also illustrated by a set of numerical experiments.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19971023) and the Natural Science Foundation of Heilongjiang Province, China.
文摘By the method of geometry of Banach spaces, we have proven that a bounded linear operatorin Banach space is a compact linear one iff it can be uniformly approximated by a sequence of the finite rankbounded homogeneous operators, which reveals the essence of the counter example given by Enflo.
文摘Banach空间中线性算子分块矩阵的广义Drazin逆不仅在矩阵理论中有着重要应用,而且在控制论、系统论和微分方程等方面也有着重要应用.因此,给出了线性算子分块矩阵x=(a bc d)∈A(其中A为B代数)的广义舒尔补s=d-ca^db是广义Drazin逆条件下此分块矩阵的广义Drazin逆的几种新特性,这些特性是广义舒尔补Drazin逆、广义舒尔补群逆和广义舒尔补为零情形下的推广形式.
文摘文章主要研究Banach代数上两个元素和的伪Drazin逆的存在性.通过Pierce分解,得到两个元素和具有伪Drazin逆的一些条件.然后,研究了Banach代数上反三角算子矩阵的伪Drazin逆的存在性,证明了反三角算子矩阵(1 b 10)∈M_(2)(A)^(■),b∈(A)^(■) 当且仅当b∈A^(■).最后,给出相应的数值例子来论证得到的结果.
