Generalizations of the c0-l1-l∞ theorem of Bessaga and Pełczyński

Let X and Y be two Banach spaces such that Y has a subsymmetric Schauder basis (yn). We study the consequences of the following assumption: X* has a subspace isomorphic to Y. If the basis is shrinking, then X* contains a copy of Y** (Proposition 1), and if X has the so-called controlled separable projection property (in particular, if X is weakly compactly determined), then X* contains a copy of [yn*]* (Theorem 1). These results are applied for Orlicz sequence spaces.