This is an announcement for the paper "Containment of $\c_{\bf 0}$ and $\ell_{\bf 1}$ in $\Pi_{\bf 1} \hbox{\bf (}\E\hbox{\bf ,}\ \F\hbox{\bf )}$" by Mohsen Alimohammady.

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 $\ell_{1}$.

Archive classification: Functional Analysis

Mathematics Subject Classification: 47B10; 46B20

Remarks: 4 pages

The source file(s), mat01.cls: 37258 bytes, mathtimy.sty: 20 bytes, pm2197new.tex: 11816 bytes, is(are) stored in gzipped form as 0607651.tar.gz with size 14kb. The corresponding postcript file has gzipped size 25kb.

Submitted from: amohsen@umz.ac.ir

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