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Vector Lattices and Integral Operators

  • S. S. Kutateladze

Part of the Mathematics and Its Applications book series (MAIA, volume 358)

Table of contents

  1. Front Matter
    Pages i-ix
  2. A. G. Kusraev, S. S. Kutateladze
    Pages 1-103
  3. A. V. Bukhvalov
    Pages 105-156
  4. B. M. Makarov
    Pages 157-278
  5. A. V. Bukhvalov, V. B. Korotkov, B. M. Makarovt
    Pages 279-346
  6. A. E. Gutman
    Pages 359-454
  7. Back Matter
    Pages 455-462

About this book

Introduction

The theory of vector lattices, stemming from the mid-thirties, is now at the stage where its main achievements are being summarized. The sweeping changes of the last two decades have changed its image completely. The range of its application was expanded and enriched so as to embrace diverse branches of the theory of functions, geometry of Banach spaces, operator theory, convex analysis, etc. Furthermore, the theory of vector lattices was impregnated with principally new tools and techniques from other sections of mathematics. These circumstances gave rise to a series of mono­ graphs treating separate aspects of the theory and oriented to specialists. At the same time, the necessity of a book intended for a wider readership, reflecting the modern diretions of research became clear. The present book is meant to be an attempt at implementing this task. Although oriented to readers making their first acquaintance with vector-lattice theory, it is composed so that the main topics dealt with in the book reach the current level of research in the field, which is of interest and import for specialists. The monograph was conceived so as to be divisible into two parts that can be read independently of one another. The first part is mainly Chapter 1, devoted to the so-called Boolean-valued analysis of vector lattices. The term designates the applica­ tion of the theory of Boolean-valued models by D. Scott, R. Solovay and P.

Keywords

Hilbert space Lattice Multiplication Volume banach spaces convolution field functional functional analysis geometry information integral operator operator theory vector lattice

Editors and affiliations

  • S. S. Kutateladze
    • 1
  1. 1.Sobolev Institute of MathematicsSiberian Branch of the Russian Academy of SciencesNovosibirskRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-009-0195-7
  • Copyright Information Springer Science+Business Media B.V. 1996
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-6571-9
  • Online ISBN 978-94-009-0195-7
  • Buy this book on publisher's site
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