Mapping Properties of $c_0$
Colloquium Mathematicum, Tome 80 (1999) no. 2, pp. 235-244
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Bessaga and Pełczyński showed that if $c_0$ embeds in the dual $X^*$ of a Banach space X, then $ℓ^1$ embeds as a complemented subspace of X. Pełczyński proved that every infinite-dimensional closed linear subspace of $ℓ^1$ contains a copy of $ℓ^1$ that is complemented in $ℓ^1$. Later, Kadec and Pełczyński proved that every non-reflexive closed linear subspace of $L^1 [0,1]$ contains a copy of $ℓ^1$ that is complemented in $L^1 [0,1]$. In this note a traditional sliding hump argument is used to establish a simple mapping property of $c_0$ which simultaneously yields extensions of the preceding theorems as corollaries. Additional classical mapping properties of $c_0$ are briefly discussed and applications are given.
@article{10_4064_cm_80_2_235_244,
author = {Paul Lewis},
title = {Mapping {Properties} of $c_0$},
journal = {Colloquium Mathematicum},
pages = {235--244},
publisher = {mathdoc},
volume = {80},
number = {2},
year = {1999},
doi = {10.4064/cm-80-2-235-244},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-80-2-235-244/}
}
Paul Lewis. Mapping Properties of $c_0$. Colloquium Mathematicum, Tome 80 (1999) no. 2, pp. 235-244. doi: 10.4064/cm-80-2-235-244
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