Article Title

Perturbation of Closed Range Operators

Authors

MOHAMMAD SAL MOSLEHIAN
GHADIR SADEGHI

DOI

10.3906/mat-0805-26

Abstract

Let T, A be operators with domains D(T) \subseteq D(A) in a normed space X. The operator A is called T-bounded if Ax \leq a x +b Tx for some a, b\geq 0 and all x \in D(T). If A has the Hyers--Ulam stability then under some suitable assumptions we show that both T and S: = A+T have the Hyers--Ulam stability. We also discuss the best constant of Hyers--Ulam stability for the operator S. Thus we establish a link between T-bounded operators and Hyers--Ulam stability.

Keywords

Hilbert space; perturbation; Hyers--Ulam stability; closed operator; semi-Fredholm operator.

First Page

143

Last Page

149

Recommended Citation

MOSLEHIAN, MOHAMMAD SAL and SADEGHI, GHADIR (2009) "Perturbation of Closed Range Operators," Turkish Journal of Mathematics: Vol. 33: No. 2, Article 5. https://doi.org/10.3906/mat-0805-26
Available at: https://journals.tubitak.gov.tr/math/vol33/iss2/5