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Espaces Vectoriels Topologiques: Chapitres 6 Et 7 by N. Bourbaki

Espaces Vectoriels Topologiques: Chapitres 6 Et 7

by N. Bourbaki
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Book cover type: Paperback
  • ISBN13: 9783032121554
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 340
  • Original Price: EUR 36.15
  • Language: French
  • Edition: N/A
  • Item Weight: 499 grams
  • BISAC Subject(s): Functional Analysis

Les Éléments de mathématique de Nicolas Bourbaki ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques.

Ce nouveau fascicule du Livre sur les Espaces vectoriels topologiques est consacré aux produits tensoriels d'espaces localement convexes, ainsi qu'à leurs applications.

Le chapitre VI expose la théorie des produits tensoriels topologiques. On y présente la notion de construction tensorielle, qui munit le produit tensoriel d'espaces localement convexes d'une topologie localement convexe. On détaille les propriétés de deux constructions tensorielles, dites minimale et maximale, et leurs utilisations pour décrire certains espaces fonctionnels usuels. Le chapitre se poursuit par l'étude des dualités et enveloppes de constructions tensorielles, puis par la démonstration de l'inégalité fondamentale de Grothendieck.

Le chapitre VII s'ouvre par l'étude des applications nucléaires entre espaces localement convexes, dont les propriétés sont analogues à celles des opérateurs définis par des noyaux continus. On y étudie des notions de trace et de déterminant pour les applications nucléaires entre espaces de Banach. Enfin, on présente la classe des espaces nucléaires, où se combinent plusieurs des thèmes du fascicule.

Le texte est complété par une note historique et de nombreux exercices.

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