Title : ( Perturbation of closed range operators )
Authors: Mohammad Sal Moslehian , Ghadir Sadeghi ,
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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 Ax ≤ a x +b Tx 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.
@article{paperid:1015360,
author = {Sal Moslehian, Mohammad and Sadeghi, Ghadir},
title = {Perturbation of closed range operators},
journal = {Turkish Journal of Mathematics},
year = {2009},
volume = {33},
number = {4},
month = {October},
issn = {1300-0098},
pages = {143--149},
numpages = {6},
keywords = {Hilbert space; perturbation; Hyers–Ulam stability; closed operator; semi-Fredholm operator.},
}
%0 Journal Article
%T Perturbation of closed range operators
%A Sal Moslehian, Mohammad
%A Sadeghi, Ghadir
%J Turkish Journal of Mathematics
%@ 1300-0098
%D 2009
