Dual Kadec-Klee norms and the relationships between Wijsman, slice, and Mosco convergence. (English) Zbl 0820.46007

This rather comprehensive article deals with interplay between the set convergences of the title. The most principal and typical result reads: Mosco and slice convergences coincide if and only if the weak-star and norm topologies agree on the dual sphere.


46B10 Duality and reflexivity in normed linear and Banach spaces
46A55 Convex sets in topological linear spaces; Choquet theory
46N10 Applications of functional analysis in optimization, convex analysis, mathematical programming, economics
46G05 Derivatives of functions in infinite-dimensional spaces
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