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February 2018 Perturbation bounds for the Moore–Penrose metric generalized inverse in some Banach spaces
Jianbing Cao, Wanqin Zhang
Ann. Funct. Anal. 9(1): 17-29 (February 2018). DOI: 10.1215/20088752-2017-0020

Abstract

Let X,Y be Banach spaces, and let T, δT:XY be bounded linear operators. Put T¯=T+δT. In this article, utilizing the gap between closed subspaces and the perturbation bounds of metric projections, we first present some error estimates of the upper bound of T¯MTM in Lp (1<p<+) spaces. Then, by using the concept of strong uniqueness and modulus of convexity, we further investigate the corresponding perturbation bound T¯MTM in uniformly convex Banach spaces.

Citation

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Jianbing Cao. Wanqin Zhang. "Perturbation bounds for the Moore–Penrose metric generalized inverse in some Banach spaces." Ann. Funct. Anal. 9 (1) 17 - 29, February 2018. https://doi.org/10.1215/20088752-2017-0020

Information

Received: 19 September 2016; Accepted: 30 January 2017; Published: February 2018
First available in Project Euclid: 12 July 2017

zbMATH: 06841338
MathSciNet: MR3758740
Digital Object Identifier: 10.1215/20088752-2017-0020

Subjects:
Primary: 47A05
Secondary: 46B20

Keywords: metric generalized inverse , metric projection , perturbation

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.9 • No. 1 • February 2018
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