Mosco convergence and the Kadec property

Borwein, Jonathan M.; Fitzpatrick, Simon

doi:10.1090/S0002-9939-1989-0969313-4

Mosco convergence and the Kadec property
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by Jonathan M. Borwein and Simon Fitzpatrick PDF

Proc. Amer. Math. Soc. 106 (1989), 843-851 Request permission

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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