Synopses & Reviews
The monograph presents a comprehensive study of positive operators between Riesz spaces and Banach lattices. It is a reprint of the book Positive Operators published by Academic Press in 1985. The book went out of print in the late 1990's and it is by now virtually impossible for interested people to find a copy of the Academic Press publication in the market. Meanwhile the subject of positive operators and Riesz spaces has found many applications in several disciplines -- including social sciences and engineering. Thus, the reprint of this book is aimed at making the book available not only to mathematicians but also to other scientists interested in the applications of positive operators. It is well known that many linear operators between Banach spaces arising in classical analysis are in fact positive operators. For this reason, in this book positive operators are studied in the setting of Riesz spaces and Banach lattices. In this monograph, positive operators are studied from the algebraic and topological points of view separately. Special emphasis is given to the compactness properties of positive operators and their relations to the order structures of the spaces the operators are acting upon. In order to make the book as self-sufficient as possible, some basic results from the theory of Riesz spaces and Banach lattices are included with proofs as needed. On the other hand, the reader is assumed to be familiar with the elementary concepts of real analysis and functional analysis. The material of the book is spread out in five chapters. The five chapters consist of nineteen sections. Each section ends with exercises that supplement its material. There are almost 300 exercises.These exercises extend and illustrate the material of the book in a concrete manner.
Synopsis
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. It is well known that many linear operators between Banach spaces arising in classical analysis are in fact positive operators. Therefore we study here positive operators in the setting of Riesz spaces and Banach lattices and from both the algebraic and topological points of view. Special emphasis is given to the compactness properties of positive operators and their relations to the order structures of the spaces the operators are acting upon. In order to make the book as self-sufficient as possible, some basic results from the theory of Riesz spaces and Banach lattices are included with proofs where necessary. However, familiarity with the elementary concepts of real analysis and functional analysis is assumed. The book is divided into five chapters, each consisting of nineteen sections all ending with exercises designed to supplement and illustrate the material.
Synopsis
Reprinted by popular demand, this monograph presents a comprehensive study of positive operators between Riesz spaces and Banach lattices. Since publication of this book in 1985, the subject of positive operators and Riesz spaces has found practical applications in disciplines including social sciences and engineering. This book examines positive operators in the setting of Riesz spaces and Banach lattices, from both the algebraic and topological points of view.
Table of Contents
Dedication. Foreword. Historical Foreword. Preface. Acknowledgements. List of Special Symbols.- 1. The Order Structure of Positive Operators.- 2. Components, Homomorphisms, and Orthomorphisms.- 3. Topological Considerations.- 4. Banach Lattices.- 5. Compactness Properties of Positive Operators.- Bibliography. Monographs.- Index.