New examples of $c_0$-saturated Banach spaces

Abstract

For every $ 1 < p < \infty $ an isomorphically polyhedral Banach space $E_p$ is constructed having an unconditional basis and admitting a quotient isomorphic to $\ell_p$. It is also shown that $E_p$ is not isomorphic to a subspace of a $C(K)$ space for every countable and compact metric space $K$.