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Polar locally convex topologies and Attouch-Wets convergence

  • Gerald Beer (a1)

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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References

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[1]Attouch, H. and Wets, R., ‘Quantitative stability of variational systems: I.’, The epigraph-ical distance, Trans. Amer. Math. Soc. 328 (1991), 695730.
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[8]Beer, G. and Lucchetti, R., ‘Convex optimization and the epi-distance topology’, Trans. Amer. Math. Soc. 327 (1991), 795813.
[9]Castaing, C. and Valadier, M., ‘Convex analysis and measurable multifunctions’, in Lecture notes in mathematics 580 (Springer-Verlag, Berlin, Heidelberg, New York, 1977).
[10]Hola, L., ‘The Attouch-Wets topology and a characterisation of normable spaces’, Bull. Austral. Math. Soc. 44 (1991), 1118.
[11]Kato, T., Perturbation theory for linear operators (Springer-Verlag, Berlin, Heidelberg, New York, 1966).
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Polar locally convex topologies and Attouch-Wets convergence

  • Gerald Beer (a1)

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