Perturbation analysis of the quasi-linear operator generalized inverse with prescribed range and kernel

2017 ◽  
Vol 11 ◽  
pp. 839-847
Author(s):  
Jianbing Cao
Keyword(s):  
Linear Operator ◽  
Perturbation Analysis ◽  
Generalized Inverse

scholarly journals The generalized condition numbers of bounded linear operators in Banach spaces

2004 ◽  
Vol 76 (2) ◽  
pp. 281-290 ◽  
Author(s):  
Guoliang Chen ◽  
Yimin Wei ◽  
Yifeng Xue
Keyword(s):  
Linear Operator ◽  
Banach Spaces ◽  
Perturbation Analysis ◽  
Bounded Linear Operator ◽  
Linear Operators ◽  
Condition Numbers ◽  
Bounded Linear ◽  
Infinite Dimensional ◽  
Ill Posed ◽  
Linear Operator Equations

AbstractFor any bounded linear operator A in a Banach space, two generalized condition numbers, k(A) and k(A) are defined in this paper. These condition numbers may be applied to the perturbation analysis for the solution of ill-posed differential equations and bounded linear operator equations in infinite dimensional Banach spaces. Different expressions for the two generalized condition numbers are discussed in this paper and applied to the perturbation analysis of the operator equation.

scholarly journals The Quasi-Linear Operator Outer Generalized Inverse with Prescribed Range and Kernel in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Jianbing Cao ◽  
Yifeng Xue
Keyword(s):  
Linear Operator ◽  
Banach Spaces ◽  
Bounded Linear Operator ◽  
Generalized Inverse ◽  
Generalized Inverses ◽  
Bounded Linear ◽  
Perturbation Problems

Let and be Banach spaces, and let be a bounded linear operator. In this paper, we first define and characterize the quasi-linear operator (resp., out) generalized inverse (resp., ) for the operator , where and are homogeneous subsets. Then, we further investigate the perturbation problems of the generalized inverses and . The results obtained in this paper extend some well-known results for linear operator generalized inverses with prescribed range and kernel.

scholarly journals Chain-finite operators and locally chain-finite operators

2001 ◽  
Vol 43 (1) ◽  
pp. 113-121
Author(s):  
Teresa Bermúdez ◽  
Antonio Martinón
Keyword(s):  
Positive Integer ◽  
Linear Operator ◽  
Banach Spaces ◽  
Bounded Linear Operator ◽  
Generalized Inverse ◽  
Algebraic Characterization ◽  
Bounded Linear ◽  
A Chain

We give algebraic conditions characterizing chain-finite operators and locally chain-finite operators on Banach spaces. For instance, it is shown that T is a chain-finite operator if and only if some power of T is relatively regular and commutes with some generalized inverse; that is there are a bounded linear operator B and a positive integer k such that TkBTk =Tk and TkB=BTk. Moreover, we obtain an algebraic characterization of locally chain-finite operators similar to (1).

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