Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

Streszczenie

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.