scholarly journals Some new perturbation results for generalized inverses of closed linear operators in Banach spaces

2012 ◽  
Vol 6 (2) ◽  
pp. 58-68 ◽  
Author(s):  
Qianglian Huang ◽  
Lanping Zhu ◽  
Jiena Yu
Keyword(s):  
Banach Spaces ◽  
Linear Operators ◽  
Generalized Inverses ◽  
New Perturbation ◽  
Closed Linear Operators

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.

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
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