Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 9, Number 3 (2018), 344-353.
On the perturbation of outer inverses of linear operators in Banach spaces
The main concern of this article is the perturbation problem for outer inverses of linear bounded operators in Banach spaces. We consider the following perturbed problem. Let with an outer inverse and with . What condition on the small perturbation can guarantee that the simplest possible expression is a generalized inverse, Moore–Penrose inverse, group inverse, or Drazin inverse of ? In this article, we give a complete solution to this problem. Since the generalized inverse, Moore–Penrose inverse, group inverse, and Drazin inverse are outer inverses, our results extend and improve many previous results in this area.
Ann. Funct. Anal., Volume 9, Number 3 (2018), 344-353.
Received: 14 April 2017
Accepted: 10 July 2017
First available in Project Euclid: 11 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Primary: 47A55: Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15]
Secondary: 47A58: Operator approximation theory
Zhu, Lanping; Pan, Weiwei; Huang, Qianglian; Yang, Shi. On the perturbation of outer inverses of linear operators in Banach spaces. Ann. Funct. Anal. 9 (2018), no. 3, 344--353. doi:10.1215/20088752-2017-0041. https://projecteuclid.org/euclid.afa/1512982817