It is an easy undergraduate exercise to show that (finite) direct sums are preserved under dualisation. Thus, it is natural to ask if we the following holds:

is it true that if $X$ is a subspace of $Y$, then $X^* $ is a subspace of $Y^*$?

In many cases this is certainly not true (one can construct relevant subspaces of $Y=\ell^\infty$) but... let me say that $Y$ has **property (D)** if the above hypothesis holds for $Y$.

Is it true that the only spaces with property (D) are Hilbert spaces?