Mendeley出力
＜図書＞
Convergence structures and applications to functional analysis
| 責任表示 | by R. Beattie and H.-P. Butzmann |
|---|---|
| データ種別 | 図書 |
| 出版情報 | Dordrecht : Kluwer Academic , c2002 |
| 本文言語 | 英語 |
| 大きさ | xiii, 264 p. ; 25 cm |
| 概要 | Convergence vector spaces and the application of continuous convergence overcome many problems inherent in other forms of functional analysis, argue Beattie (mathematics and computer science, Mount Al...ison U., Canada) and Butzmann (mathematics and information science, U. Mannheim, Germany). After introducing the basic theory of convergence spaces and convergence vector spaces, they describe a number of functional analytic applications, specifically related to continuous convergence as a duality structure, the Hahn-Banach extension theorem, the closed graph theorem, the Banach- Steinhaus theorem, and duality and reflexivity for convergence groups. Annotation (c)2003 Book News, Inc., Portland, OR (booknews.com) 続きを見る |
| 目次 | Machine generated contents note: 1 Convergence spaces 1.1 Prelim inaries 1.2 Initial and final convergence structures 1.3 Special convergence spaces, modifications 1.4 Compactness 1.5 The continuous convergence structure 1.6 Countability properties and sequences in convergence spaces 1.7 Sequential convergence structures 1.8 Categorical aspects 2 Uniform convergence spaces 2.1 Generalities on uniform convergence spaces 2.2 Initial and final uniform convergence structures 2.3 Complete uniform convergence spaces 2.4 The Arzela-Ascoli thedrem 2.5 The uniform convergence structure of a convergence group 3 Convergence vector spaces 3.1 Convergence groups 3.2 Generalities on convergence vector spaces 3.3 Initial and final vector space convergence structures 3.4 Projective and inductive limits of convergence vector spaces 3.5 The locally convex topological modification 3.6 Countability axioms for convergence vector spaces 3.7 Boundedness 3.8 Notes on bornological vector spaces 4 Duality 4.1 The dual of a convergence vector space 4.2 Reflexivity 4.3 The dual of a locally convex topological vector space 4.4 An application of continuous duality 4.5 Notes 5 Hahn-Banach extension theorems 5.1 General results 5.2 Hahn-Banach spaces 5.3 Extending to the adherence 5.4 Strong Hahn-Banach spaces 5.5 An application to partial differential equations 5.6 Notes 6 The closed graph theorem 6.1 Ultracompleteness 6.2 The main theorems 6.3 An application to web spaces 7 The Banach-Steinhaus theorem 7.1 Equicontinuous sets 7.2 Banach-Steinhaus pairs 7.3 The continuity of bilinear mappings 8 Duality theory for convergence groups 8.1 Reflexivity 8.2 Duality for convergence vector spaces 8.3 Subgroups and quotient groups 8.4 Topological groups 8.5 Groups of unimodular continuous functions 8.6 c- and co-duality for topological groups.続きを見る |
| 電子版へのリンク | https://hdl.handle.net/2324/6882643 |
所蔵情報
| 状態 | 巻次 | 所蔵場所 | 請求記号 | 刷年 | 文庫名称 | 資料番号 | コメント | 予約・取寄 | 複写申込 | 自動書庫 |
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理系図3F 数理独自 | BEAT/10/1 | 2002 |
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023212002002536 |
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書誌詳細
| 一般注記 | Includes bibliographical references (p. 247-256) and index |
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| 著者標目 | *Beattie, R. Butzmann, H.-P. |
| 書誌ID | 1001392766 |
| ISBN | 1402005660 |
| NCID | BA57108995 |
| 巻冊次 | ISBN:1402005660 |
| 登録日 | 2009.11.02 |
| 更新日 | 2009.11.02 |