Title of article :
Perturbation of Closed Range Operators
Author/Authors :
Moslehian, Mohammad Sal ferdowsi university of mashhad - Center of Excellence in Analysis on Algebraic Structures (CEAAS) - Department of Pure Mathematics, مشهد, ايران , Sadeghi, Ghadir ferdowsi university of mashhad - Center of Excellence in Analysis on Algebraic Structures (CEAAS) - Department of Pure Mathematics, مشهد, ايران
Abstract :
Let T,A be operators with domains D(T) ⊆ D(A) in a normed space X. The operator A is called T -bounded if IIAxII ≤ aIIxII+ b IITxII for some a, b ≥ 0 and all x ∈ 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.
Journal title :
Turkish Journal of Mathematics
Journal title :
Turkish Journal of Mathematics
