Polar locally convex topologies and Attouch-Wets convergence

Publisher： Cambridge University Press

E-ISSN： 1755-1633|46|1|33-46

ISSN： 0004-9727

Source： Bulletin of the Australian Mathematical Society, Vol.46, Iss.1, 1992-08, pp. : 33-46

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Abstract

Let X be a Hausdorff locally convex space. We show that convergence of a net of continuous linear functionals on X with respect to a given polar topology on its continuous dual X′ can be explained in terms of the convergence of the corresponding net of its graphs in X × R, and the corresponding net of level sets at a fixed height in X, with respect to a natural generalisation of Attouch-Wets convergence in normable spaces.

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