Adjective
normable (not comparable)
Capable of being normed.
A topological vector space is normable if and only if it is Hausdorff and has a convex bounded neighborhood of 0. http://eom. Source: Internet
More strongly: a topological vector space is said to be normable if its topology can be induced by a norm. Source: Internet
On the other hand, infinite-dimensional Montel spaces are never normable. Source: Internet