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Spaces of vector-valued functions and their duals

✍ Scribed by Walter Roth

Publisher
John Wiley and Sons
Year
2012
Tongue
English
Weight
284 KB
Volume
285
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

We consider spaces of continuous vector‐valued functions on a locally compact Hausdorff space, endowed with classes of locally convex topologies, which include and generalize various known ones such as weighted space‐ or inductive limit‐type topologies. The main result states that every continuous linear functional on such a function space can be expressed as an integral with respect to some canonical (dual space‐valued) vector measure.

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