Barrelled Locally Convex Spaces, Volume 131

1st Edition

Authors: P. Pérez Carreras J. Bonet
Hardcover ISBN: 9780444701299
eBook ISBN: 9780080872421
Imprint: North Holland
Published Date: 1st March 1987
Page Count: 511
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Table of Contents

1. Baire Linear Spaces. 2. Basic Tools. 3. Barrels and Discs. 4. Barrelled Spaces. 5. Local Completeness. 6. Bornological and Ultrabornological Spaces. 7. B- and Br-Completeness. 8. Inductive Limit Topologies. 9. Strong Barrelledness Conditions. 10. Locally Convex Properties of the Space of Continuous Functions Endowed with the Compact-Open Topology. 11. Barrelledness Conditions on Topological Tensor Products. 12. Holomorphically Significant Properties of Locally Convex Spaces. 13. A Short Collection of Open Problems. A Table of Barrelled Spaces. References. Index.

Description

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.


Details

No. of pages:
511
Language:
English
Copyright:
© North Holland 1987
Published:
Imprint:
North Holland
eBook ISBN:
9780080872421
Hardcover ISBN:
9780444701299

Reviews

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.


About the Authors

P. Pérez Carreras Author

J. Bonet Author