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.
Author(s): Pedro Pérez Carreras and José Bonet (Eds.)
Series: North-Holland Mathematics Studies 131
Publisher: Elsevier Science Ltd
Year: 1987
Language: English
Pages: ii-xii, 1-512
Content:
Editor
Page ii
Edited by
Page iii
Copyright page
Page iv
Dedication
Page v
Introduction
Pages vii-xii
Pedro Pérez Carreras, José Bonet
Chapter 0 Notations and Preliminaries
Pages 1-8
Chapter One Baire Linear Spaces
Pages 9-31
Chapter Two Basic Tools
Pages 33-79
Chapter Three Barrels and Discs
Pages 81-94
Chapter Four Barrelled Spaces
Pages 95-149
Chapter Five Local Completeness
Pages 151-165
Chapter Six Bornological and Ultrabornological Spaces
Pages 167-197
Chapter Seven B- and Br-Completeness
Pages 199-224
Chapter Eight Inductive Limit Topologies
Pages 225-331
Chapter Nine Strong Barrelledness Conditions
Pages 333-368
Chapter Ten Locally Convex Properties of the Space of Continuous Functions Endowed with the Compact-Open Topology
Pages 369-379
Chapter Eleven Barrelledness Conditions on Topological Tensor Products
Pages 381-447
Chapter Twelve Holomorphically Significant Properties of Locally Convex Spaces
Pages 449-475
Chapter Thirteen A Short Collection of Open Problems
Pages 477-479
A Table of Barrelled Spaces
Page 481
Book References in the Text
Page 483
References
Pages 484-506
Tables
Page 507
Index
Pages 509-511
Abbreviations and Symbols
Page 512
