Spectral value sets of closed linear operators

2000 ◽  
Vol 456 (1998) ◽  
pp. 1397-1418 ◽  
Author(s):  
E. Gallestey ◽  
D. Hinrichsen ◽  
A. J. Pritchard
Keyword(s):  
Linear Operators ◽  
Value Sets ◽  
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.

A Note on the Adjoint of the Product of Operators

1970 ◽  
Vol 13 (1) ◽  
pp. 39-45
Author(s):  
Chia-Shiang Lin
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Closed Subspace ◽  
Linear Operators ◽  
Finite Codimension ◽  
Restricted Condition ◽  
Closed Linear Operators

Cordes and Labrousse ([2] p. 697), and Kaniel and Schechter ([6] p. 429) showed that if S and T are domain-dense closed linear operators on a Hilbert space H into itself, the range of S is closed in H and the codimension of the range of S is finite, then, (TS)* = S*T*. With a somewhat different approach and more restricted condition on S, the same assertion was obtained by Holland [5] recently, that S is a bounded everywhere-defined linear operator whose range is a closed subspace of finite codimension in H.

Periodic Solutions of Second Order Degenerate Differential Equations with Delay in Banach Spaces

2018 ◽  
Vol 61 (4) ◽  
pp. 717-737 ◽  
Author(s):  
Shangquan Bu ◽  
Gang Cai
Keyword(s):  
Sufficient Conditions ◽  
Complex Banach Space ◽  
Second Order ◽  
Linear Operators ◽  
Bounded Linear ◽  
Order Degenerate ◽  
Degenerate Differential Equations ◽  
Necessary And Sufficient ◽  
Equations With Delay ◽  
Closed Linear Operators

AbstractWe give necessary and sufficient conditions of the Lp-well-posedness (resp. -wellposedness) for the second order degenerate differential equation with finite delayswith periodic boundary conditions (Mu)(0) = (Mu)(2π), (Mu)′ (0) = (Mu)′ (2π), where A, B, and M are closed linear operators on a complex Banach space X satisfying D(A) ∩ D(B) ⊂ D(M), F and G are bounded linear operators from into X.

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