IJPAM: Volume 84, No. 5 (2013)
Slovak Academy of Sciences
Štefánikova 49, SK-814 73 Bratislava, SLOVAKIA
Abstract. The present paper is concerned with some representatons of linear mappings of continuous functions into locally convex vector spaces, namely
Theorem. If X is a complete Hausdorff locally convex vector space, then a general form of weakly compact mapping T:C[a,b] → X is of the form Tg=∫abg(t)dx(t), where the function x(⋅):[a,b] → X has a weakly compact semivariation on [a,b].
This theorem is a generalization of the result from Banach spaces to locally convex vector spaces.
Received: December 5, 2012
AMS Subject Classification: 28E10, 81P10
Key Words and Phrases: locally convex space, weakly compact semivariation, vector measure on Borel subsets
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DOI: 10.12732/ijpam.v84i5.10 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395