Relationship between the Hyers-Ulam stability and the Moore-Penrose inverse
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
Cite
@article{arxiv.1211.0192,
title = {Relationship between the Hyers-Ulam stability and the Moore-Penrose inverse},
author = {Qianglian Huang and Mohammad Sal Moslehian},
journal= {arXiv preprint arXiv:1211.0192},
year = {2013}
}
Comments
16 pages, to appear in the Electronic Journal of Linear Algebra (ELA)