Banach spaces whose duals contain complemented subspaces isomorphic to C[0, 1]

On Nonseparable Banach Spaces

“…Theorems C and D imply an affirmative answer to a problem by Hagler and Stegall [7]; in conjunction with the counterexample by Haydon, mentioned above, it follows that the Hagler-Stegall conjecture is independent of Z.F.C. for a = w+.…”

“…The space Za has been introduced in [7] by Hagler and StegaU; it is useful in the study of dual spaces; in fact, Stegall has proved in [18] that an isomorphic embedding of Za into a Banach space X implies an isomorphism between (C(-l, 1}°)* and a complemented subspace of X*.…”

“…So X* contains a complemented subspace isomorphic to L'(0, 1), and it follows from [7] that X contains the space Z.…”

Complemented isometric copies of $L_{1}$ in dual Banach spaces

“…The proof may be found in [HS,Lemma 2] (although the statement of that result is not as precise as the lemma given here). See [LR] for the definition and properties of L 1 spaces.…”

“…The key to constructing a Banach space Y and an operator T : X → Y to which Lemma 4 can be applied is the following technical lemma, which is an amplified version of [HS,Lemma 3]. In this lemma, the isometric copy of L 1 in X * is used to construct the sets A n , which in turn readily yield an asymptotically isometric copy of 1 in X.…”