The Bartle-Dunford-Schwartz Integral : Integration with Respect to a Sigma-Additive Vector Measure
In 1953, Grothendieck [G] characterized locally convex Hausdor? spaces which have the Dunford-Pettis property and used this property to characterize weakly compact operators u : C(K)? F,where K is a compact Hausdor? space and F is a locally convex Hausdor? space (brie?y, lcHs) which is complete. Amo...
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Livre numérique |
| Lingua: | Anglais |
| Pubblicazione: |
Basel :
Birkhäuser Basel
[20..].
Cham : Springer Nature |
| Edizione: | 1st ed. 2008. |
| Serie: | Monografie Matematyczne
69 |
| Soggetti: | |
| Accesso online: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
L'impression du document génère 310 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • The Bartle-Dunford-Schwartz Integral, Texte imprimé, 9783764394684 • The Bartle-Dunford-Schwartz integral, integration with respect to a sigma-additive vector measure, T.V. Panchapagesan, 2008, Basel, Birkhäuser, 1 vol. (XV- 301 p.), Monografie matematyczne, 978-3-7643-8601-6 |
| Riassunto: | In 1953, Grothendieck [G] characterized locally convex Hausdor? spaces which have the Dunford-Pettis property and used this property to characterize weakly compact operators u : C(K)? F,where K is a compact Hausdor? space and F is a locally convex Hausdor? space (brie?y, lcHs) which is complete. Among other results, he also showedthat there is a bijective correspondencebetween the family of all F-valued weakly compact operators u on C(K) and that of all F-valued ?-additive Baire measures on K. But he did not develop any theory of integration to represent these operators. Later, in 1955, Bartle, Dunford, and Schwartz [BDS] developed a theory of integration for scalar functions with respect to a ?-additive Banach-space-valued vector measure m de?ned on a ?-algebra of sets and used it to give an integral representationfor weakly compact operatorsu : C(S)? X,where S is a compact Hausdor? space and X is a Banach space. A modi?ed form of this theory is given inSection10ofChapterIVof[DS1].Inhonoroftheseauthors,we callthe integral introduced by them as well as its variants given in Section 2.2 of Chapter 2 and in Section 4.2 of Chapter 4, the Bartle-Dunford-Schwartz integral or brie?y, the BDS-integral |
|---|---|
| Descrizione del documento: | L'impression du document génère 310 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Bibliografia: | Bibliogr. Index |
| ISBN: | 9783764386023 |
| ISSN: | 2297-0274 |
| Accesso: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |