Abstract
Let X be a quasicomplete locally convex Hausdorff space. Let T be a locally compact Hausdorff space and let C 0(T) =\(\left\{ {f:T \to \mathbb{C},\;f} \right.\) is continuous and vanishes at infinity} be endowed with the supremum norm. Starting with the Borel extension theorem for X-valued \(\sigma\)-additive Baire measures on T, an alternative proof is given to obtain all the characterizations given in [13] for a continuous linear map \(u:C_0 \left( T \right) \to X\) to be weakly compact.
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Panchapagesan, T.V. A Borel extension approach to weakly compact operators on C 0(T). Czechoslovak Mathematical Journal 52, 97–115 (2002). https://doi.org/10.1023/A:1021775405507
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DOI: https://doi.org/10.1023/A:1021775405507