A simple proof of the Borel extension theorem and weak compactness of operators

Ivan Dobrakov; Thiruvaiyaru V. Panchapagesan

A Borel extension approach to weakly compact operators on $C_{0} (T)$

Thiruvaiyaru V. Panchapagesan (2002)

Czechoslovak Mathematical Journal

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Let $X$ be a quasicomplete locally convex Hausdorff space. Let $T$ be a locally compact Hausdorff space and let $C_{0} (T) = {f T \to I$ , $f$ is continuous and vanishes at infinity $}$ be endowed with the supremum norm. Starting with the Borel extension theorem for $X$ -valued $σ$ -additive Baire measures on $T$ , an alternative proof is given to obtain all the characterizations given in [13] for a continuous linear map $u C_{0} (T) \to X$ to be weakly compact.

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