<電子ブック>
Boolean Valued Analysis / by A.G. Kusraev, Semën Samsonovich Kutateladze
(Mathematics and Its Applications ; 494)
版 | 1st ed. 1999. |
---|---|
出版者 | Dordrecht : Springer Netherlands : Imprint: Springer |
出版年 | 1999 |
本文言語 | 英語 |
大きさ | XII, 332 p : online resource |
著者標目 | *Kusraev, A.G author Kutateladze, Semën Samsonovich author SpringerLink (Online service) |
件 名 | LCSH:Difference equations LCSH:Functional equations LCSH:Operator theory FREE:Difference and Functional Equations FREE:Operator Theory |
一般注記 | 1. Universes of Sets -- § 1.1. Boolean Algebras -- § 1.2. Representation of a Boolean Algebra -- § 1.3. Von Neumann—Gödel—Bernays Theory -- § 1.4. Ordinals -- § 1.5. Hierarchies of Sets -- 2. Boolean Valued Universes -- § 2.1. The Universe over a Boolean Algebra -- § 2.2. Transformations of a Boolean Valued Universe -- § 2.3. Mixing and the Maximum Principle -- § 2.4. The Transfer Principle -- § 2.5. Separated Boolean Valued Universes -- 3. Functors of Boolean Valued Analysis -- § 3.1. The Canonical Embedding -- § 3.2. The Descent Functor -- § 3.3. The Ascent Functor -- § 3.4. The Immersion Functor -- § 3.5. Interplay Between the Main Functors -- 4. Boolean Valued Analysis of Algebraic Systems -- § 4.1. Algebraic B-Systems -- § 4.2. The Descent of an Algebraic System -- § 4.3. Immersion of Algebraic B-Systems -- § 4.4. Ordered Algebraic Systems -- § 4.5. The Descent of a Field -- 5. Boolean Valued Analysis of Banach Spaces -- § 5.1. Vector Lattices -- § 5.2. Representation of Vector Lattices -- § 5.3. Lattice Normed Spaces -- § 5.4. The Descent of a Banach Space -- § 5.5. Spaces with Mixed Norm -- 6. Boolean Valued Analysis of Banach Algebras -- § 6.1. The Descent of a Banach Algebra -- § 6.2. AW*-Algebras and AW*-Modules -- § 6.3. The Boolean Dimension of an AW*-Module -- § 6.4. Representation of an AW*-Module -- § 6.5. Representation of a Type I AW*-Algebra -- § 6.6. Embeddable C*-Algebras -- References Boolean valued analysis is a technique for studying properties of an arbitrary mathematical object by comparing its representations in two different set-theoretic models whose construction utilises principally distinct Boolean algebras. The use of two models for studying a single object is a characteristic of the so-called non-standard methods of analysis. Application of Boolean valued models to problems of analysis rests ultimately on the procedures of ascending and descending, the two natural functors acting between a new Boolean valued universe and the von Neumann universe. This book demonstrates the main advantages of Boolean valued analysis which provides the tools for transforming, for example, function spaces to subsets of the reals, operators to functionals, and vector-functions to numerical mappings. Boolean valued representations of algebraic systems, Banach spaces, and involutive algebras are examined thoroughly. Audience: This volume is intended for classical analysts seeking powerful new tools, and for model theorists in search of challenging applications of nonstandard models HTTP:URL=https://doi.org/10.1007/978-94-011-4443-8 |
目次/あらすじ
所蔵情報を非表示
電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
電子ブック | オンライン | 電子ブック |
|
|
Springer eBooks | 9789401144438 |
|
電子リソース |
|
EB00239280 |
類似資料
この資料の利用統計
このページへのアクセス回数:7回
※2017年9月4日以降