## Annals of Functional Analysis

### Perturbation bounds for the Moore–Penrose metric generalized inverse in some Banach spaces

#### Abstract

Let $X,Y$ be Banach spaces, and let $T$, $\delta T:X\to Y$ be bounded linear operators. Put $\bar{T}=T+\delta T$. 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 $\Vert \bar{T}^{M}-T^{M}\Vert$ in $L^{p}$ ($1\lt p\lt +\infty$) spaces. Then, by using the concept of strong uniqueness and modulus of convexity, we further investigate the corresponding perturbation bound $\Vert \bar{T}^{M}-T^{M}\Vert$ in uniformly convex Banach spaces.

#### Article information

Source
Ann. Funct. Anal., Volume 9, Number 1 (2018), 17-29.

Dates
Accepted: 30 January 2017
First available in Project Euclid: 12 July 2017

https://projecteuclid.org/euclid.afa/1499824816

Digital Object Identifier
doi:10.1215/20088752-2017-0020

Mathematical Reviews number (MathSciNet)
MR3758740

Zentralblatt MATH identifier
06841338

#### Citation

Cao, Jianbing; Zhang, Wanqin. Perturbation bounds for the Moore–Penrose metric generalized inverse in some Banach spaces. Ann. Funct. Anal. 9 (2018), no. 1, 17--29. doi:10.1215/20088752-2017-0020. https://projecteuclid.org/euclid.afa/1499824816

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