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. [1] [2]
That 2. implies 1. is an application of the Banach–Alaoglu theorem, setting to the Weak-* topology. That 1. implies 2. is an application of the Bipolar theorem.
Let be a pointed metric space with distinguished point denoted . The Dixmier-Ng Theorem is applied to show that the Lipschitz space of all real-valued Lipschitz functions from to that vanish at (endowed with the Lipschitz constant as norm) is a dual Banach space. [3]
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. [1] [2]
That 2. implies 1. is an application of the Banach–Alaoglu theorem, setting to the Weak-* topology. That 1. implies 2. is an application of the Bipolar theorem.
Let be a pointed metric space with distinguished point denoted . The Dixmier-Ng Theorem is applied to show that the Lipschitz space of all real-valued Lipschitz functions from to that vanish at (endowed with the Lipschitz constant as norm) is a dual Banach space. [3]