## Annals of Functional Analysis

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

### 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 $\overline{T}=T+\delta T$. 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 {\overline{T}}^{M}-{T}^{M}\Vert $ in ${L}^{p}$ ($1<p<+\infty $) spaces. Then, by using the concept of strong uniqueness and modulus of convexity, we further investigate the corresponding perturbation bound $\Vert {\overline{T}}^{M}-{T}^{M}\Vert $ in uniformly convex Banach spaces.

#### Article information

**Source**

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

**Dates**

Received: 19 September 2016

Accepted: 30 January 2017

First available in Project Euclid: 12 July 2017

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.1215/20088752-2017-0020

**Mathematical Reviews number (MathSciNet)**

MR3758740

**Zentralblatt MATH identifier**

06841338

**Subjects**

Primary: 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.)

Secondary: 46B20: Geometry and structure of normed linear spaces

**Keywords**

metric generalized inverse perturbation metric projection

#### 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