Duality theory of spaces of vector-valued continuous functions
Marian Nowak, Aleksandra Rzepka (2005)
Commentationes Mathematicae Universitatis Carolinae
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Let be a completely regular Hausdorff space, a real normed space, and let be the space of all bounded continuous -valued functions on . We develop the general duality theory of the space endowed with locally solid topologies; in particular with the strict topologies for . As an application, we consider criteria for relative weak-star compactness in the spaces of vector measures for . It is shown that if a subset of is relatively -compact, then the set is still...