Turkish Journal of Mathematics
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.
DOI
10.3906/mat-0805-26
Keywords
Hilbert space; perturbation; Hyers--Ulam stability; closed operator; semi-Fredholm operator.
First Page
143
Last Page
149
Recommended Citation
MOSLEHIAN, M. S, & SADEGHI, G (2009). Perturbation of Closed Range Operators. Turkish Journal of Mathematics 33 (2): 143-149. https://doi.org/10.3906/mat-0805-26
