Dual Topology - Characterization of Dual Topologies

Characterization of Dual Topologies

The Mackey–Arens theorem, named after George Mackey and Richard Arens, characterizes all possible dual topologies on a locally convex spaces.

The theorem shows that the coarsest dual topology is the weak topology, the topology of uniform convergence on all finite subsets of, and the finest topology is the Mackey topology, the topology of uniform convergence on all weakly compact subsets of .

Read more about this topic:  Dual Topology

Other articles related to "characterization of dual topologies, dual":

mackey–arens_theorem" class="article_title_2">Dual Topology - Characterization of Dual Topologies - Mackey–Arens Theorem
... Given a dual pair with a locally convex space and its continuous dual then is a dual topology on if and only if it is a topology of uniform convergence on a family of absolutely convex ...

Famous quotes containing the word dual:

    Thee for my recitative,
    Thee in the driving storm even as now, the snow, the winter-day
    declining,
    Thee in thy panoply, thy measur’d dual throbbing and thy beat
    convulsive,
    Thy black cylindric body, golden brass and silvery steel,
    Walt Whitman (1819–1892)