Boolean Valued Analysis

✍ Scribed by A. G. Kusraev, S. S. Kutateladze (auth.)

• Publisher: Springer Netherlands
• Year: 1999
• Tongue: English
• Leaves: 330
• Series: Mathematics and Its Applications 494
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xii
Universes of Sets....Pages 1-40
Boolean Valued Universes....Pages 41-88
Functors of Boolean Valued Analysis....Pages 89-140
Boolean Valued Analysis of Algebraic Systems....Pages 141-198
Boolean Valued Analysis of Banach Spaces....Pages 199-250
Boolean Valued Analysis of Banach Algebras....Pages 251-280
Back Matter....Pages 281-332

✦ Subjects

Difference and Functional Equations; Operator Theory