  In this paper we study ways to establish when a Banach space can be
identified as the dual or the double dual of another Banach space. To obtain
these results, we relate these spaces with other, concrete Banach spaces -
tipically $\ell^1$ and $\ell^\infty$ - and show that under suitable assumptions
we can transfer properties of these spaces to the space we consider. In
particular, we show how these results can be used to obtain in a simple way
interesting results about spaces such as $BMO$ and $BV$.
