UID:
almahu_9949697286702882
Format:
1 online resource (529 p.)
ISBN:
1-281-79793-6
,
9786611797935
,
0-08-087242-5
Series Statement:
North-Holland mathematics studies ; 131
Content:
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-analytic techniques.Beginning with some basic and important results in different branches of Analysis, the volume deals with Baire spaces, presents a variety of techniques, and gives the necessary definitions, exploring conditions on discs to ensure that they are absorbed by the barrels of the sp
Note:
Description based upon print version of record.
,
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 Fréchet spaces; 2.3 Biorthogonal systems and transversal subspaces; 2.4 The three-space problem for Fréchet spaces; 2.5 Some results on separability
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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
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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
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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
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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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11.6 Projective tensor products of Fréchet and (DF)-spaces (an introduction)
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English
Additional Edition:
ISBN 0-444-70129-X
Language:
English
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