Perturbation of Closed Range Operators

Authors : Mohammad Sal MOSLEHIAN, Ghadir SADEGHI

Pages : 143-149

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Let T, A be operators with domains Dinsert ignore into journalissuearticles values(T); \subseteq Dinsert ignore into journalissuearticles values(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 Dinsert ignore into journalissuearticles values(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