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2015 Weak approximation properties of subspaces
Ju Myung Kim, Keun Young Lee
Banach J. Math. Anal. 9(2): 248-252 (2015). DOI: 10.15352/bjma/09-2-16

Abstract

The paper is concerned with weak approximation properties which are weaker than the classical approximation property. For $\lambda \geq 1$, we prove that a Banach space $X$ has the $\lambda$-bounded weak approximation property ($\lambda$-BWAP) if and only if every locally $1$-complemented subspace of $X$ has the $\lambda$-BWAP, and that if $X$ has the $\lambda$-BWAP and $Z$ is a locally $\mu$-complemented subspace of $X$, then $Z$ has the $(2\mu+4)\mu\lambda$-BWAP. It also follows that $X$ has the weak approximation property (WAP) if and only if every locally complemented subspace of $X$ has the WAP.

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Ju Myung Kim. Keun Young Lee. "Weak approximation properties of subspaces." Banach J. Math. Anal. 9 (2) 248 - 252, 2015. https://doi.org/10.15352/bjma/09-2-16

Information

Published: 2015
First available in Project Euclid: 19 December 2014

zbMATH: 1325.46018
MathSciNet: MR3296116
Digital Object Identifier: 10.15352/bjma/09-2-16

Subjects:
Primary: 46B28
Secondary: 47L20

Keywords: ‎approximation property‎‎ , bounded weak approximation property , weak approximation property

Rights: Copyright © 2015 Tusi Mathematical Research Group

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Vol.9 • No. 2 • 2015
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