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A Borel extension approach to weakly compact operators on $C_0(T)$
Czechoslovak Mathematical Journal, Tome 52 (2002) no. 1, pp. 97-115 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $X$ be a quasicomplete locally convex Hausdorff space. Let $T$ be a locally compact Hausdorff space and let $C_0(T) = \lbrace f\: T \rightarrow I$, $f$ is continuous and vanishes at infinity$\rbrace $ 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 $u\: C_0(T) \rightarrow X$ to be weakly compact.
Let $X$ be a quasicomplete locally convex Hausdorff space. Let $T$ be a locally compact Hausdorff space and let $C_0(T) = \lbrace f\: T \rightarrow I$, $f$ is continuous and vanishes at infinity$\rbrace $ 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 $u\: C_0(T) \rightarrow X$ to be weakly compact.
Classification : 28B05, 46G10, 47B07, 47B38 
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Panchapagesan, T. V. A Borel extension approach to weakly compact operators on $C_0(T)$. Czechoslovak Mathematical Journal, Tome 52 (2002) no. 1, pp. 97-115. http://geodesic.mathdoc.fr/item/CMJ_2002_52_1_a9/

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