Copies of c0(Г) and ℓ∞(Г)/c0(Г) in quotients of Banach spaces with applications to Orlicz and Marcinkiewicz spaces

Let X be a Banach space, let Y be its subspace, and let Г be an infinite set. We study the consequences of the assumption that an operator T embeds ℓ221E;(Г) into X isomorphically with T(c0(Г)) ⊂ Y. Under additional assumptions on T we prove the existence of isomorphic copies of c0(Гℵ0) in X/Y, and complemented copies ℓ∞(Г) in X/Y. In concrete cases we obtain a new information about the structure of X/Y. In particular, L∞[O,1]/C[O,1] contains a complemented copy of ℓ∞/c0, and some natural (lattice) quotients of real Orlicz and Marcinkiewicz spaces contain lattice-isometric and positively I-complemented copies of(real) ℓ∞/c0.