Containment of $\c_0$ and $\ell_1$ in $\Pi_1(E,F)$

Mohsen Alimohammady

Containment of $\c_0$ and $\ell_1$ in $\Pi_1(E,F)$

Functional Analysis 2007-05-23 v1

Authors: 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 $\ell_1$ .

Keywords

absolutely 1-summing operators Banach spaces copies of c0 copies of l1 complemented subspace

Cite

@article{arxiv.math/0607651,
  title  = {Containment of $\c_0$ and $\ell_1$ in $\Pi_1(E,F)$},
  author = {Mohsen Alimohammady},
  journal= {arXiv preprint arXiv:math/0607651},
  year   = {2007}
}

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4 pages

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