Geodesic
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.
DOI : 10.4064/cm-80-2-235-244

Paul Lewis 1

1 
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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. http://geodesic.mathdoc.fr/articles/10.4064/cm-80-2-235-244/

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