Turkish Journal of Mathematics

Perturbation of Closed Range Operators
Mohammad Sal MOSLEHIAN^1,2, Ghadir SADEGHI^1,2
¹Department of Pure Mathematics,
Ferdowsi University of Mashhad, P. O. Box
1159, Mashhad 91775, IRAN
e-mail: moslehian@ferdowsi.um.ac.ir and moslehian@ams.org
²Center of Excellence in Analysis
on Algebraic Structures (CEAAS),
Ferdowsi University of
Mashhad-IRAN
e-mail: ghadir54@yahoo.com

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.

Key Words: Hilbert space; perturbation; Hyers--Ulam stability; closed operator; semi-Fredholm operator.

Turk. J. Math., 33, (2009), 143-149.
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Other articles published in the same issue: Turk. J. Math.,vol.33,iss.2.