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Mosco convergence and the Kadec property

Authors: Jonathan M. Borwein and Simon Fitzpatrick
Journal: Proc. Amer. Math. Soc. 106 (1989), 843-851
MSC: Primary 46B20; Secondary 52A05, 54C60
MathSciNet review: 969313
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Abstract: We study the relationship between Wijsman convergence and Mosco convergence for sequences of convex sets. Our central result is that Mosco convergence and Wijsman convergence coincide for sequences of convex sets if and only if the underlying space is reflexive with the dual norm having the Kadec property.

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