If X is a normed linear space, then the set of continuous linear functionals on X is called the dual (or conjugate) space of X. When equipped with the norm left double bracketing bar f right double bracketing bar = sup{ left bracketing bar f(x) right bracketing bar : left double bracketing bar x right double bracketing bar = 1}, a dual normed space is a Banach space.

Banach space | dual vector space