In functional analysis, the Dixmier–Ng theorem is a characterization of when a normed space is in fact a dual Banach space.
It was proven by Kung-fu Ng, who called it a variant of a theorem proven earlier by Jacques Dixmier.
That 1. implies 2. is an application of the Bipolar theorem.
The Dixmier-Ng Theorem is applied to show that the Lipschitz space
(endowed with the Lipschitz constant as norm) is a dual Banach space.