Stable Perturbation Of Densely—Defined Closed Operators On Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Qianglian Huang ◽  
Lanping Zhu ◽  
Xiaoru Chen ◽  
Chang Zhang

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.


Author(s):  
W. D. Evans

SynopsisLetL0,M0be closed densely defined linear operators in a Hilbert spaceHwhich form an adjoint pair, i.e.. In this paper, we study closed operatorsSwhich satisfyand are regularly solvable in the sense of Višik. The abstract results obtained are applied to operators generated by second-order linear differential expressions in a weighted spaceL2(a, b; w).


Author(s):  
L. E. Labuschagne

SynopsisThe stability of several natural subsets of the bounded non-semi-Fredholm operators undercompact perturbations were studied by R. Bouldin [2] in separable Hilbert spaces and by M. Gonzales and V. M. Onieva [6] in Banach spaces. The aim of this paper is to study this problem for closed operators in operator ranges. The main results are a characterisation of the non-semi-Fredholm operators with respect to α-closed and α-compact operators as well as a generalisation of a result of M. Goldman [5]. We also give some applications of the theory developed to ordinary differential operators.


2013 ◽  
Vol 06 (02) ◽  
pp. 1350025 ◽  
Author(s):  
Kishor D. Kucche ◽  
M. B. Dhakne

In this paper we establish the controllability result for class of mixed Volterra–Fredholm neutral functional integrodifferential equations in Banach spaces where the linear part is non-densely defined and satisfies the resolvent estimate of the Hille–Yosida condition. The results are obtained using the integrated semigroup theory and the Sadovskii's fixed point theorem.


1993 ◽  
Vol 113 (1) ◽  
pp. 173-177 ◽  
Author(s):  
Mostafa Mbekhta

AbstractThe Laffey–West theorem concerning finite rank perturbations of bounded Fredholm operators is extended to closed densely defined operators on Banach Spaces.


2009 ◽  
Vol 3 (1) ◽  
pp. 39-45 ◽  
Author(s):  
M. Frank ◽  
P. Găvruţa ◽  
M.S. Moslehian

We define the notion of ?-perturbation of a densely defined adjointable mapping and prove that any such mapping f between Hilbert A-modules over a fixed C*-algebra A with densely defined corresponding mapping g is A-linear and adjointable in the classical sense with adjoint g. If both f and g are every- where defined then they are bounded. Our work concerns with the concept of Hyers-Ulam-Rassias stability originated from the Th. M. Rassias' stability theorem that appeared in his paper [On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300]. We also indicate complementary results in the case where the Hilbert C?-modules admit non-adjointable C*-linear mappings.


1973 ◽  
Vol 13 (2) ◽  
pp. 107-124 ◽  
Author(s):  
Michael Reed ◽  
Barry Simon

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