Annals of Functional Analysis

On the perturbation of outer inverses of linear operators in Banach spaces

Lanping Zhu, Weiwei Pan, Qianglian Huang, and Shi Yang

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Abstract

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 TB(X,Y) with an outer inverse T{2}B(Y,X) and δTB(X,Y) with δTT{2}<1. What condition on the small perturbation δT can guarantee that the simplest possible expression B=T{2}(I+δTT{2})1 is a generalized inverse, Moore–Penrose inverse, group inverse, or Drazin inverse of T+δT? 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.

Article information

Source
Ann. Funct. Anal., Advance publication (2018), 10 pages.

Dates
Received: 14 April 2017
Accepted: 10 July 2017
First available in Project Euclid: 11 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.afa/1512982817

Digital Object Identifier
doi:10.1215/20088752-2017-0041

Subjects
Primary: 47A55: Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15]
Secondary: 47A58: Operator approximation theory

Keywords
outer inverse generalized inverse Moore–Penrose inverse group inverse simplest possible expression

Citation

Zhu, Lanping; Pan, Weiwei; Huang, Qianglian; Yang, Shi. On the perturbation of outer inverses of linear operators in Banach spaces. Ann. Funct. Anal., advance publication, 11 December 2017. doi:10.1215/20088752-2017-0041. https://projecteuclid.org/euclid.afa/1512982817


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