scholarly journals On Stable Perturbations of the Generalized Drazin Inverses of Closed Linear Operators in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Qianglian Huang ◽  
Lanping Zhu ◽  
Xiaoru Chen ◽  
Chang Zhang
Keyword(s):  
Banach Spaces ◽  
Null Space ◽  
Linear Operators ◽  
Special Cases ◽  
Stable Perturbation ◽  
Closed Linear Operators

We investigate the stable perturbation of the generalized Drazin inverses of closed linear operators in Banach spaces and obtain some new characterizations for the generalized Drazin inverses to have prescribed range and null space. As special cases of our results, we recover the perturbation theorems of Wei and Wang, Castro and Koliha, Rakocevic and Wei, Castro and Koliha and Wei.

On the null spaces of linear Fredholm operators depending on several parameters

1978 ◽  
Vol 84 (1) ◽  
pp. 131-142 ◽  
Author(s):  
M. Shearer
Keyword(s):  
Banach Spaces ◽  
Fredholm Operator ◽  
Bifurcation Theory ◽  
Null Space ◽  
Parameter Family ◽  
Linear Operators ◽  
Fredholm Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear

AbstractLet X, Y be real Banach spaces, and let = {f(λ):λ ∈ m} be an m-parameter family of bounded linear operators from X to Y, with f(λ) depending continuously on λ. The cases m = 1 and m = 2 are considered, and conditions on are found which determine the null space of f(λ) for all λ near a given λ0 such that f(λ0): X → Y is a Fredholm operator. The results obtained are shown to be of particular interest in perturbed bifurcation theory.

Computable and Continuous Partial Homomorphisms on Metric Partial Algebras

2003 ◽  
Vol 9 (3) ◽  
pp. 299-334 ◽  
Author(s):  
Viggo Stoltenberg-Hansen ◽  
John V. Tucker
Keyword(s):  
Banach Spaces ◽  
Effective Properties ◽  
Equivalence Theorem ◽  
Linear Operators ◽  
General Situation ◽  
Universal Algebras ◽  
Effective Metric ◽  
Partial Algebras ◽  
General Equivalence Theorem ◽  
Closed Linear Operators

AbstractWe analyse the connection between the computability and continuity of functions in the case of homomorphisms between topological algebraic structures. Inspired by the Pour-El and Richards equivalence theorem between computability and boundedness for closed linear operators on Banach spaces, we study the rather general situation of partial homomorphisms between metric partial universal algebras. First, we develop a set of basic notions and results that reveal some of the delicate algebraic, topological and effective properties of partial algebras. Our main computability concepts are based on numerations and include those of effective metric partial algebras and effective partial homomorphisms. We prove a general equivalence theorem that includes a version of the Pour-El and Richards Theorem, and has other applications. Finally, the Pour-El and Richards axioms for computable sequence structures on Banach spaces are generalised to computable partial sequence structures on metric algebras, and we prove their equivalence with our computability model based on numerations.

scholarly journals Closed linear operators between nonarchimedean Banach spaces

2005 ◽  
Vol 16 (2) ◽  
pp. 201-214
Author(s):  
Hernán R. Henríquez ◽  
Samuel Navarro H. ◽  
Jose Aguayo G.
Keyword(s):  
Banach Spaces ◽  
Linear Operators ◽  
Closed Linear Operators

Regularizers of Closed Operators

1974 ◽  
Vol 17 (1) ◽  
pp. 67-71 ◽  
Author(s):  
C.-S. Lin
Keyword(s):  
Banach Spaces ◽  
Compact Operator ◽  
Null Space ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Closed Operators

Let X and Y be two Banach spaces and let B(X, Y) denote the set of bounded linear operators with domain X and range in 7. For T∈B(X, Y), let N(T) denote the null space and R(T) the range of T. J. I. Nieto [5, p. 64] has proved the following two interesting results. An operator T∈B(X, Y) has a left regularizer, i.e., there exists a Q∈B(Y, X) such that QT=I+A, where I is the identity on X and A∈B(X, X) is a compact operator, if and only if dim N(T)<∞ and R(T) has a closed complement.

Equisummability for linear operators in Banach spaces

1987 ◽  
Vol 106 (3-4) ◽  
pp. 315-325
Author(s):  
M. A. Kon ◽  
A. G. Ramm ◽  
L. A. Raphael
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Analytic Functions ◽  
Elliptic Operators ◽  
Second Order ◽  
Linear Operators ◽  
Abstract Setting ◽  
Second Order Elliptic Operators ◽  
Closed Linear Operators

SynopsisLet A and B be closed linear operators on a Banach space X. Assume that ε(εI – A)−1f→f as |ε|→ ∞ for all f in X, ζ∊∑ ⊂ℂ. Under what conditions on B − A does the same relationship hold for B? When does [ε(εI − A)−1 − ε(εI − B)−1 ] f→ 0 in some stronger norm than that of X? The questions are discussed in an abstract setting and the results are generalised to other analytic functions of A. Applications are given to second order elliptic operators.

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