Perturbation of Closed Range Operators
Authors : Mohammad Sal Moslehian, Ghadir Sadeghi
Pages : 143-149
View : 10 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
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.