Abstract: A well known result of Pelczynski states that if c_0 embeds in a dual Banach space then l_\infty embeds as well. We will show that if c_0 embeds in the space of the weakly compact operators between two Banach spaces in a non-trivial way, then l_\infty embeds as well. There are interesting open problems related to this result. This result is extracted from a paper of G. Emmanuele. The proofs are very easy so this seminar will be accessible to the graduate students who are encouraged to attend!