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.
Hilbert space; perturbation; Hyers--Ulam stability; closed operator; semi-Fredholm operator.
MOSLEHIAN, MOHAMMAD SAL and SADEGHI, GHADIR
"Perturbation of Closed Range Operators,"
Turkish Journal of Mathematics: Vol. 33:
2, Article 5.
Available at: https://journals.tubitak.gov.tr/math/vol33/iss2/5