Containment of $\c_0$ and $\ell_1$ in $Π_1(E,F)$

Details Containment of $\c_0$ and $\ell_1$ in $Π_1(E,F)$ Containment of $\c_0$ and $\ell_1$ in $Π_1(E,F)$

2006-07-26

arxiv.org/abs/math/0607651v1

Mathematics

Functional Analysis

4 pages

Scientific paper

Suppose $\Pi_1(E, F)$ is the space of all absolutely 1-summing operators
between two Banach spaces $E$ and $F$. We show that if $F$ has a copy of $c_0$,
then $\Pi_1(E, F)$ will have a copy of $c_0$, and under some conditions if $E$
has a copy of $\ell_1$ then $\Pi_1(E, F)$ would have a complemented copy of
$\ell_1$.

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