Title : ( Relationship between the Hyers--Ulam stability and the Moore--Penrose inverse )
Authors: Qianglian Huang , Mohammad Sal Moslehian ,
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Abstract
In this paper, we establish a link between the Hyers--Ulam stability and the Moore--Penrose inverse, that is, a closed operator has the Hyers--Ulam stability if and only if it has a bounded Moore--Penrose inverse. Meanwhile, the stability constant can be determined in terms of the Moore--Penrose inverse. Based on this result, some conditions for the perturbed operators having the Hyers--Ulam stability are obtained and the Hyers--Ulam stability constant is expressed explicitly in the case of closed operators. In the case of the bounded linear operators we obtain some characterizations for the Hyers--Ulam stability constants to be continuous. As an application, we give a characterization for the Hyers--Ulam stability constants of the semi-Fredholm operators to be continuous.
Keywords
, Hyers, , Ulam stability; Moore, , Penrose inverse; generalized inverse; reduced minimum modulus; closed linear operator; $T, $boundedness; semi, Fredholm operator
@article{paperid:1031003,
author = {Qianglian Huang and Sal Moslehian, Mohammad},
title = {Relationship between the Hyers--Ulam stability and the Moore--Penrose inverse},
journal = {Electronic Journal of Linear Algebra},
year = {2012},
volume = {23},
number = {1},
month = {November},
issn = {1537-9582},
pages = {891--905},
numpages = {14},
keywords = {Hyers--Ulam stability; Moore--Penrose inverse; generalized
inverse; reduced minimum modulus; closed linear operator;
$T-$boundedness; semi-Fredholm operator},
}
%0 Journal Article
%T Relationship between the Hyers--Ulam stability and the Moore--Penrose inverse
%A Qianglian Huang
%A Sal Moslehian, Mohammad
%J Electronic Journal of Linear Algebra
%@ 1537-9582
%D 2012
