Abstract
The relation between the free Banach lattice generated by a Banach space and free dual spaces is clarified. In particular, it is shown that for every Banach space E the free p-convex Banach lattice generated by E⁎⁎, denoted FBL(p)[E⁎⁎], admits a canonical isometric lattice embedding into FBL(p)[E]⁎⁎ and FBL(p)[E⁎⁎] is lattice finitely representable in FBL(p)[E]. Moreover, we also show that for p>1, FBL(p)[E]⁎⁎ can actually be considered as the free dual p-convex Banach lattice generated by E, whereas for p=1 this happens precisely when E does not contain complemented copies of ℓ1.
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