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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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

Ann. Funct. Anal. (2018), 10 pages.

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

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Digital Object Identifier

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

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


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.

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