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Panchapagesan,T.V.";"On weakly compact operators on

Donato, Andrea (2000) Panchapagesan,T.V.";"On weakly compact operators on. Memorie scientifiche di Andrea Donato, LXXVIII. pp. 41-56.


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Let T be a locally compact Hausdorff space and let C0(T)={f:T-->C|f is continuous and vanishes at infinity} 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 [6] and by combining the integration technique of Bartle-Dunford-Schwartz [1],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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Item Type: Article
Subjects: M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Scienze Fisiche, Matematiche e Naturali
Depositing User: Utente Interno
Date Deposited: 01 Jun 2004
Last Modified: 13 Apr 2010 09:38

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