Positive Operators / Edition 1

Positive Operators / Edition 1

by Charalambos D. Aliprantis, Owen Burkinshaw
     
 

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ISBN-10: 1402050070

ISBN-13: 9781402050077

Pub. Date: 10/31/2006

Publisher: Springer Netherlands

Reprinted by popular demand, this monograph presents a comprehensive study of positive operators between Riesz spaces and Banach lattices. Since the first publication of this book, (Academic Press, 1985), the subject of positive operators and Riesz spaces has found many applications in several disciplines, including social sciences and engineering.

Overview

Reprinted by popular demand, this monograph presents a comprehensive study of positive operators between Riesz spaces and Banach lattices. Since the first publication of this book, (Academic Press, 1985), the subject of positive operators and Riesz spaces has found many applications in several disciplines, including social sciences and engineering.

Product Details

ISBN-13:
9781402050077
Publisher:
Springer Netherlands
Publication date:
10/31/2006
Edition description:
1st ed. 1985. Corr. 2nd printing 2006
Pages:
376
Product dimensions:
6.50(w) x 9.50(h) x 1.10(d)

Table of Contents

Foreword ix

Historical Foreword xi

Preface xiii

Acknowledgments xv

List of Special Symbols xvii

Chapter 1 The Order Structure of Positive Operators 1

§1.1 Basic Properties of Positive Operators 1

§1.2 Extensions of Positive Operators 23

§1.3 Order Projections 31

§1.4 Order Continuous Operators 45

§1.5 Positive Linear Functionals 58

Chapter 2 Components, Homomorphisms, and Orthomorphisms 79

§2.1 The Components of a Positive Operator 80

§2.2 Lattice Homomorphisms 93

§2.3 Orthomorphisms 111

Chapter 3 Topological Considerations 133

§3.1 Topological Vector Spaces 133

§3.2 Weak Topologies on Banach Spaces 156

§3.3 Locally Convex-Solid Riesz Spaces 169

Chapter 4 Banach Lattices 181

§4.1 Banach Lattices with Order Continuous Norms 181

§4.2 Weak Compactness in Banach Lattices 207

§4.3 Embedding Banach Spaces 221

§4.4 Banach Lattices of Operators 254

Chapter 5 Compactness Properties of Positive Operators 273

§5.1 Compact Operators 273

§5.2 Weakly Compact Operators 290

§5.3 L- and M-weakly Compact Operators 316

§5.4 Dunford-Pettis Operators 340

Bibliography 359

Monographs 369

Index 371

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