  This is the second part in a series dealing with subspaces of de Branges
spaces of entire function generated by majorization on subsets of the closed
upper half-plane. In this part we investigate certain Banach spaces generated
by admissible majorants. We study their interplay with the original de Branges
space structure, and their geometry. In particular, we will show that,
generically, they will be nonreflexive and nonseparable.
