Mackey space
From Wikipedia, the free encyclopedia
In mathematics, particularly in functional analysis, a Mackey space is a locally convex topological vector space X such that the topology of X coincides with the Mackey topology τ(X,X′), the finest topology which still preserves the continuous dual. They are named after George Mackey.
Examples of locally convex spaces that are Mackey spaces include:
- All barrelled spaces [1] and more generally all infrabarreled spaces [2]
- Hence in particular all bornological spaces [1] and reflexive spaces
- All metrizable spaces.[1]
- In particular, all Fréchet spaces, including all Banach spaces and specifically Hilbert spaces, are Mackey spaces.
- The product, locally convex direct sum, and the inductive limit of a family of Mackey spaces is a Mackey space.[3]
