Annals of Functional Analysis

A new characterization of the bounded approximation property

Ju Myung Kim and Keun Young Lee

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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 (Sα) of finite-rank operators from Z to X with SαλT such that lim αSαzTz=0 for every zZ.

Article information

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

Received: 22 March 2016
Accepted: 24 June 2016
First available in Project Euclid: 5 October 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46B28: Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20]
Secondary: 47L20: Operator ideals [See also 47B10]

bounded approximation property bounded compact approximation property separable Banach space


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.

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