## Annals of Functional Analysis

### A new characterization of the bounded approximation property

#### Abstract

We prove that a Banach space $X$ has the bounded approximation property if and only if, for every separable Banach space $Z$ and every injective operator $T$ from $Z$ to $X$, there exists a net $(S_{\alpha})$ of finite-rank operators from $Z$ to $X$ with $\|S_{\alpha}\|\leq\lambda_{T}$ such that $\lim_{\alpha}\|S_{\alpha}z-Tz\|=0$ for every $z\in Z$.

#### Article information

Source
Ann. Funct. Anal., Volume 7, Number 4 (2016), 672-677.

Dates
Accepted: 24 June 2016
First available in Project Euclid: 5 October 2016

https://projecteuclid.org/euclid.afa/1475685113

Digital Object Identifier
doi:10.1215/20088752-3661116

Mathematical Reviews number (MathSciNet)
MR3555758

Zentralblatt MATH identifier
1360.46013

#### Citation

Kim, Ju Myung; Lee, Keun Young. A new characterization of the bounded approximation property. Ann. Funct. Anal. 7 (2016), no. 4, 672--677. doi:10.1215/20088752-3661116. https://projecteuclid.org/euclid.afa/1475685113

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