Mackey–Arens theorem

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The Mackey–Arens theorem is an important theorem in functional analysis that characterizes those locally convex vector topologies that have some given space of linear functionals as their continuous dual space. According to Narici (2011), this profound result is central to duality theory; a theory that is "the central part of the modern theory of topological vector spaces."[1]

Prerequisites[]

Main articles: Polar topology and Mackey topology

Let X be a vector space and let Y be a vector subspace of the algebraic dual of X that separates points on X. If