A note on Banach spaces with l1-saturated duals
نویسنده
چکیده
Let E and F be Banach spaces. We say that E is F -saturated if every infinite dimensional closed subspace of E contains an isomorphic copy of F . In [2], it is shown that there exists a c0-saturated Banach space with an unconditional basis whose dual contains an isomorphic copy of l2. In this note, we give an example where the dual situation occurs. It is shown that there is a Banach space with an unconditional basis which contains an isomorphic copy of l2, and whose dual is l1-saturated. We follow standard Banach space terminology as used in [3]. Our example is a certain subspace of the weak L2 space L2,∞[0,∞). Recall that this is the space of all measurable functions f on [0,∞) such that
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