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Spaces of vector‐valued functions and their duals
Author(s) -
Roth Walter
Publication year - 2012
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201100085
Subject(s) - mathematics , hausdorff space , locally convex topological vector space , dual polyhedron , dual pair , continuous functions on a compact hausdorff space , function space , locally compact space , dual space , normed vector space , vector space , pure mathematics , topological vector space , space (punctuation) , reflexive space , topology (electrical circuits) , topological space , interpolation space , topological tensor product , combinatorics , functional analysis , biochemistry , chemistry , linguistics , philosophy , gene
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.