Donato, Andrea (2000) Panchapagesan,T.V.";"On weakly compact operators on. Memorie scientifiche di Andrea Donato, LXXVIII. pp. 41-56.
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Abstract
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.
| 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 |
| URI: | http://cab.unime.it/mus/id/eprint/95 |
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