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Barrelled locally convex spaces /
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-analy...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Amsterdam ; New York : New York, N.Y., U.S.A. :
North-Holland ; Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.,
1987.
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| Colección: | North-Holland mathematics studies ;
131. Notas de matem�atica (Rio de Janeiro, Brazil) ; no. 113. |
| Temas: | |
| Acceso en línea: | Texto completo Texto completo Texto completo |
MARC
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| 100 | 1 | |a P�erez Carreras, Pedro. | |
| 245 | 1 | 0 | |a Barrelled locally convex spaces / |c Pedro P�erez Carreras, Jos�e Bonet. |
| 260 | |a Amsterdam ; |a New York : |b North-Holland ; |a New York, N.Y., U.S.A. : |b Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., |c 1987. | ||
| 300 | |a 1 online resource (xv, 512 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a North-Holland mathematics studies ; |v 131 | |
| 490 | 1 | |a Notas de matem�atica ; |v 113 | |
| 520 | |a 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. | ||
| 504 | |a Includes bibliographical references (pages 484-506) and index. | ||
| 588 | 0 | |a Print version record. | |
| 506 | |3 Use copy |f Restrictions unspecified |2 star |5 MiAaHDL | ||
| 533 | |a Electronic reproduction. |b [Place of publication not identified] : |c HathiTrust Digital Library, |d 2011. |5 MiAaHDL | ||
| 538 | |a 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. |u http://purl.oclc.org/DLF/benchrepro0212 |5 MiAaHDL | ||
| 583 | 1 | |a digitized |c 2011 |h HathiTrust Digital Library |l committed to preserve |2 pda |5 MiAaHDL | |
| 505 | 0 | |a 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 Fr�echet spaces; 2.3 Biorthogonal systems and transversal subspaces; 2.4 The three-space problem for Fr�echet spaces; 2.5 Some results on separability | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 546 | |a English. | ||
| 650 | 0 | |a Barrelled spaces. | |
| 650 | 0 | |a Locally convex spaces. | |
| 650 | 6 | |a Espaces tonnel�es. |0 (CaQQLa)201-0094592 | |
| 650 | 6 | |a Espaces localement convexes. |0 (CaQQLa)201-0041963 | |
| 650 | 7 | |a MATHEMATICS |x Transformations. |2 bisacsh | |
| 650 | 7 | |a Barrelled spaces |2 fast |0 (OCoLC)fst00827745 | |
| 650 | 7 | |a Locally convex spaces |2 fast |0 (OCoLC)fst01001674 | |
| 650 | 7 | |a Lokalkonvexer Raum |2 gnd |0 (DE-588)4168126-5 | |
| 650 | 7 | |a Tonnelierter Raum |2 gnd |0 (DE-588)4300598-6 | |
| 700 | 1 | |a Bonet, Jos�e. | |
| 776 | 0 | 8 | |i Print version: |a P�erez Carreras, Pedro. |t Barrelled locally convex spaces. |d 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 |z 044470129X |z 9780444701299 |w (DLC) 87130041 |w (OCoLC)15624086 |
| 830 | 0 | |a North-Holland mathematics studies ; |v 131. | |
| 830 | 0 | |a Notas de matem�atica (Rio de Janeiro, Brazil) ; |v no. 113. | |
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| 856 | 4 | 0 | |u https://sciencedirect.uam.elogim.com/science/publication?issn=03040208&volume=131 |z Texto completo |
| 856 | 4 | 0 | |u https://sciencedirect.uam.elogim.com/science/bookseries/03040208/131 |z Texto completo |