Donato, Andrea (2000) Panchapagesan,T.V.";"On weakly compact operators on. Memorie scientifiche di Andrea Donato, LXXVIII. pp. 41-56.
Let T be a locally compact Hausdorff space and let C0(T)= be provided with the supremum norm.Let X be a quasicomplete locally convex Hausdorff space.Suppose u : C0(T) -->X is a continuous linear operator.By refining the method adopted by Grothendick in  and by combining the integration technique of Bartle-Dunford-Schwartz ,are obtained 32 characterizations for the operator u to be weakly compact,several of which are new.The present method is so powerful as to deduce the isolated result of Dinculeanu and Kluvanek on the regular Borel extension of o-additive locally convex space valued Baire measures as corollary of the main characterization theorem.Also is included an elegant proof of the range theorem of Tweddle on o-additive vector measures.
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