Containment of $\c_0$ and ${\ell }_1$ in ${\Pi }_1(E,F)$

Abstract

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 ${\ell }_1$.

arXiv comment4 pages