Subspaces and quotient spaces of $$(\Sigma G_n )_{l_p } $$ and $$(\Sigma G_n )_{c_0 } $$

Abstract

Let (Gn) be a sequence which is dense (in the sense of the Banach-Mazur distance coefficient) in the class of all finite dimensional Banach spaces. Set\(C_p = (\Sigma G_n )_{l_p } (1< p< \infty ) = (\Sigma G_n )_{c_0 } \). It is shown that a Banach spaceX is isomorphic to a subspace ofCp (1<p≦∞) if and only ifX is isomorphic to a quotient space ofCp.