Barrelled Locally Convex Spaces

Przednia okładka
Elsevier, 1 mar 1987 - 511
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 space.

The abstract theory of barrelled spaces is then presented, as well as local completeness and its applications to the inheritance of the Mackey topology to subspaces. Further discussed is the abstract study of bornological and ultrabornological spaces; B- and Br-completeness; inductive limits; strong barrelledness conditions; characterizations of barrelled, bornological and (DF)-spaces in the context of spaces of type C(X); the stability of barrelledness conditions of topological tensor products and the related questions of commutability of inductive limits and tensor products; and the holomorphically significant properties of locally convex spaces as developed by Nachbin and others.

 

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Spis treści

CHAPTER 0 NOTATIONS AND PRELIMINARIES
1
CHAPTER 1 BAIRE LINEAR SPACES
9
CHAPTER 2 BASIC TOOLS
33
CHAPTER 3 BARRELS AND DISCS
81
CHAPTER 4 BARRELLED SPACES
95
CHAPTER 5 LOCAL COMPLETENESS
151
CHAPTER 6 BORNOLOGICAL AND ULTRABORNOLOGICAL SPACES
167
CHAPTER 7 B AND BrCOMPLETENESS
199
CHAPTER 11 BARRELLEDNESS CONDITIONS ON TOPOLOGICAL TENSOR PRODUCTS
381
CHAPTER 12 HOLOMORPHICALLY SIGNIFICANT PROPERTIES OF LOCALLY CONVEX SPACES
449
CHAPTER 13 A SHORT COLLECTION OF OPEN PROBLEMS
477
A TABLE OF BARRELLED SPACES
481
BOOK REFERENCES I N THE TEXT
483
REFERENCES
484
TABLES
507
INDEX
509

CHAPTER 8 INDUCTlVE LIMIT TOPOLOGIES
225
CHAPTER 9 STRONG BARRELLEDNESS CONDITIONS
333
CHAPTER 10 LOCALLY CONVEX PROPERTIES OF THE SPACE OF CONTINUOUS FUNCTIONS ENDOWED WITH THE COMPACTOPEN T...
369
ABBREVIATIONS and SYMBOLS
512
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