Turkish Journal of Mathematics
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
