Panchapagesan, T.V. (1995) On weakly compact operators on $C_0(T)$. Accademia Peloritana dei Pericolanti, Classe di Scienze FF. MM. NN., LXXIII. pp. 4156.

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Abstract
Let $T$ be a locally compact Hausdorff space and let $C_0(T)={f:T \to \ \mathbb{C} \f$ is continuous and vanishes at infinity } be provided with the supremum norm.Let $X$ be a quasicomplete locally convex Hausdorff space. Suppose $u:C_0(T) \to \ X$ is a continuous linear operator. By refining the method adopted by Grothendick in [6] and by combining the integration technique of BartleDunfordSchwartz [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 $ \sigma \ $ 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 \sigma additive vector measures.
Item Type:  Article 

Subjects:  M.U.S.  Miscellanea > Atti Accademia Peloritana > Classe di Scienze Fisiche, Matematiche e Naturali > 1995 M.U.S.  Miscellanea > Atti Accademia Peloritana > Classe di Scienze MedicoBiologiche > 1995 M.U.S.  Miscellanea > Atti Accademia Peloritana > Classe di Scienze Giuridiche, Economiche e Politiche > 1995 M.U.S.  Miscellanea > Atti Accademia Peloritana > Classe di Lettere, Filosofia e belle Arti > 1995 
Depositing User:  Dr A F 
Date Deposited:  19 Sep 2012 07:53 
Last Modified:  19 Sep 2012 07:53 
URI:  http://cab.unime.it/mus/id/eprint/616 
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