دانلود کتاب Barrelled Locally Convex Spaces (Volume 131) (North-Holland Mathematics Studies, Volume 131)

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Barrelled Locally Convex Spaces
Copyright Page
Introduction
TABLE OF CONTENTS
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 Fréchet spaces
2.3 Biorthogonal systems and transversal subspaces
2.4 The three-space problem for Fréchet spaces
2.5 Some results on separability
2.6 Some results concerning the space KN
2.7 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 COMPLETENESS
5.1 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 TOPOLOGIES
8.1 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 Remarks
CHAPTER 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
11.6 Projective tensor products of Fréchet and (DF)-spaces (an introduction)
11.7 NACHBIN\'s weighted spaces of continous functions
11.8 The space of continuous functions with compact support
11.9 Projective descriptions of weighted inductive limits
11.10 Notes and Remarks
CHAPTER 12 – HOLOMORPHICALLY SIGNIFICANT PROPERTIES OF LOCALLY CONVEX SPACES
12.1 Preliminaries
12.2 Examples
12.3 Notes and Remarks
CHAPTER 13 – A SHORT COLLECTION OF OPEN PROBLEMS
A TABLE OF BARRELLED SPACES
BOOK REFERENCES I N THE TEXT
REFERENCES
TABLES
INDEX
ABBREVIATIONS and SYMBOLS