Given a complex Banach space $X$ and its antidual $\hat X^*$, it is possible in some cases to apply the complex interpolation method, and get as $(X,\hat X^*)_{1/2}$ a Hilbert space. See [F. Watbled, Complex interpolation of a Banach space and its dual, Math. Scand. 87 (2000), 200-210].
I am trying to understand the case when $X$ has a Schauder basis, in which $X$ and $\hat X^*$ can be seen as spaces of complex sequences. Following Watbled's paper, the key to get $(X,\hat X^*)_{1/2}=\ell_2$ is to show that the spaces satisfy the following property:
(H)$\quad$ $\ell_2$ is continuously embedded in $X+\hat X^*$.
I would like to know under which conditions the space $X$ satisfies (H); in particular if it does when the basis is unconditional.