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Barrelled locally convex spaces

Author: Pedro Pérez Carreras; José Bonet
Publisher: Amsterdam ; New York : North-Holland ; New York, N.Y., U.S.A. : Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1987.
Series: North-Holland mathematics studies, 131.; Notas de matemática (Rio de Janeiro, Brazil), no. 113.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Pérez Carreras, Pedro.
Barrelled locally convex spaces.
Amsterdam ; New York : North-Holland ; New York, N.Y., U.S.A. : Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1987
(DLC) 87130041
(OCoLC)15624086
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Pedro Pérez Carreras; José Bonet
ISBN: 9780444701299 044470129X 9780080872421 0080872425 1281797936 9781281797933
OCLC Number: 316549601
Reproduction Notes: Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2011. MiAaHDL
Description: 1 online resource (xv, 512 pages) : illustrations.
Details: Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
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 B r -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.
Series Title: North-Holland mathematics studies, 131.; Notas de matemática (Rio de Janeiro, Brazil), no. 113.
Responsibility: Pedro Pérez Carreras, José Bonet.

Abstract:

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 B-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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