Barrelled locally convex spaces /

This book is a systematic treatment of barrelled spaces, and of structures in which barrelledness conditions are significant. It is a fairly self-contained study of the structural theory of those spaces, concentrating on the basic phenomena in the theory, and presenting a variety of functional-analy...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: P�erez Carreras, Pedro
Otros Autores: Bonet, Jos�e
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Amsterdam ; New York : New York, N.Y., U.S.A. : North-Holland ; Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1987.
Colección:North-Holland mathematics studies ; 131.
Notas de matem�atica (Rio de Janeiro, Brazil) ; no. 113.
Temas:
Barrelled spaces.
Locally convex spaces.
Espaces tonnel�es.
Espaces localement convexes.
MATHEMATICS > Transformations.
Barrelled spaces
Locally convex spaces
Lokalkonvexer Raum
Tonnelierter Raum
Acceso en línea:Texto completo
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Tabla de Contenidos:
  • Front Cover; Barrelled Locally Convex Spaces; Copyright Page; TABLE OF CONTENTS; Introduction; CHAPTER 0
  • NOTATIONS AND PRELIMINARIES; CHAPTER 1
  • BAIRE LINEAR SPACES; 1.1 Topological Preliminaries; 1.2 Baire linear spaces; 1.3 Some examples of metrizable locally convex spaces which are not Baire; 1.4 Notes and Remarks; CHAPTER 2
  • BASIC TOOLS; 2.1 The sliding-hump technique; 2.2 Linearly independent sequences in Fr�echet spaces; 2.3 Biorthogonal systems and transversal subspaces; 2.4 The three-space problem for Fr�echet spaces; 2.5 Some results on separability
  • 2.6 Some results concerning the space KN2.7 Notes and Remarks; CHAPTER 3
  • BARRELS AND DISCS; 3.1 Barrels; 3.2 The space EB. Banach discs; 3 .3 Some Lemmata; 3.4 Notes and Remarks; CHAPTER 4
  • BARRELLED SPACES; 4.1 Definitions and characterizations; 4.2 Permanence properties I; 4.3 Permanence properties II; 4.4 Nearly closed sets, polar topologies and the barrelled topology associated to a given topology; 4.5 Barrelled enlargements; 4.6 Some examples of non-barrelled spaces; 4.7 Some examples of barrelled spaces; 4.8 Barrelled vector-valued sequence spaces; 4.9 Notes and Remarks
  • CHAPTER 5
  • LOCAL COMPLETENESS5.1 Definitions and characterizations; 5.2 Stability of Mackey spaces; 5.3 Notes and Remarks; CHAPTER 6
  • BORNOLOGICAL AND ULTRABORNOLOGICAL SPACES; 6.1 Definitions and characterizations; 6.2 Permanence properties I; 6.3 Permanence properties II; 6.4 Examples; 6.5 Representing ultrabornological spaces; 6.6 Notes and Remarks; CHAPTER 7
  • B- AND Br-COMPLETENESS; 7.1 The duality closed graph theorem; 7.2 B- and Br -complete spaces; 7.3 Non-Br -complete spaces; 7.4 A Br -complete space which is not B-complete; 7.5 Notes and Remarks
  • CHAPTER 8
  • INDUCTlVE LIMIT TOPOLOGIES8.1 Generalized inductive limits; 8.2 Weak barrelledness conditions; 8.3 (DF)-and (gDF)-spaces; 8.4 Countable inductive limits of Hausdorff locally convex spaces: Generalities . Strict inductive limits; 8.5 Regularity conditions in countable inductive limits; 8.6 An introduction to welI
  • located and limit subspaces; 8.7 Non-complete metrizabie and normable (LF)-spaces; 8.8 Completions and quotients of (LF)-spaces; 8.9 Notes and Remarks; CHAPTER 9
  • STRONG BARRELLEDNESS CONDITIONS; 9.1 Definitions and main results; 9.2 Permanence properties; 9.3 Examples
  • 9.4 Notes and RemarksCHAPTER 10
  • LOCALLY CONVEX PROPERTIES OF THE SPACE OF CONTINUOUS FUNCTIONS ENDOWED WITH THE COMPACT-OPEN TOPOLOGY; 10.1 Main results; 10.2 Notes and Remarks; CHAPTER 11
  • BARRELLEDNESS CONDITIONS ON TOPOLOGICAL TENSOR PRODUCTS; 11.1 Projective tensor products and the closed graph theorem; 11.2 Strong barrelledness conditions and projective tensor products; 11.3 The bi-hypocontinuous topology; 11.4 Tensornorm topologies (a short and not too detailed account); 11.5 Locally convex properties and the injective tensor product

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