Stable Perturbation Of Densely—Defined Closed Operators On Banach Spaces

2012 ◽  
pp. 61-94
Keyword(s):  
Banach Spaces ◽  
Closed Operators ◽  
Stable Perturbation ◽  
Densely Defined

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.

Regularly solvable extensions of non-self-adjoint ordinary differential operators

1984 ◽  
Vol 97 ◽  
pp. 79-95 ◽  
Author(s):  
W. D. Evans
Keyword(s):  
Hilbert Space ◽  
Weighted Space ◽  
Differential Operators ◽  
Linear Operators ◽  
Order Linear ◽  
Adjoint Pair ◽  
Closed Operators ◽  
Ordinary Differential Operators ◽  
Linear Differential ◽  
Densely Defined

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).

On the instability of non-semi-Fredholm closed operators under compact perturbations with applications to ordinary differential operators

1988 ◽  
Vol 109 (1-2) ◽  
pp. 97-108 ◽  
Author(s):  
L. E. Labuschagne
Keyword(s):  
Banach Spaces ◽  
Hilbert Spaces ◽  
Differential Operators ◽  
Compact Operators ◽  
Fredholm Operators ◽  
Closed Operators ◽  
Compact Perturbations ◽  
Ordinary Differential Operators ◽  
The Stability

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.

CONTROLLABILITY OF NON-DENSELY DEFINED ABSTRACT MIXED VOLTERRA–FREDHOLM NEUTRAL FUNCTIONAL INTEGRODIFFERENTIAL EQUATIONS

2013 ◽  
Vol 06 (02) ◽  
pp. 1350025 ◽  
Author(s):  
Kishor D. Kucche ◽  
M. B. Dhakne
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Semigroup Theory ◽  
Linear Part ◽  
Integrodifferential Equations ◽  
Resolvent Estimate ◽  
Densely Defined ◽  
Controllability Result

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.

Semi-Fredholm perturbations and commutators

1993 ◽  
Vol 113 (1) ◽  
pp. 173-177 ◽  
Author(s):  
Mostafa Mbekhta
Keyword(s):  
Banach Spaces ◽  
Finite Rank ◽  
Fredholm Operators ◽  
Densely Defined ◽  
Fredholm Perturbations

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

scholarly journals Superstability of adjointable mappings on Hilbert c∗-modules

2009 ◽  
Vol 3 (1) ◽  
pp. 39-45 ◽  
Author(s):  
M. Frank ◽  
P. Găvruţa ◽  
M.S. Moslehian
Keyword(s):  
Banach Spaces ◽  
Linear Mapping ◽  
Stability Theorem ◽  
Classical Sense ◽  
C Algebra ◽  
The Stability ◽  
Densely Defined ◽  
Rassias Stability

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.

scholarly journals Tensor products of closed operators on Banach spaces

1973 ◽  
Vol 13 (2) ◽  
pp. 107-124 ◽  
Author(s):  
Michael Reed ◽  
Barry Simon
Keyword(s):  
Banach Spaces ◽  
Tensor Products ◽  
Closed Operators
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