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Positive Operators

ISBN-10: 1402050070

ISBN-13: 9781402050077

Edition: 2006

Authors: Charalambos D. Aliprantis, Owen Burkinshaw

List price: $119.99
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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.
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Book details

List price: $119.99
Copyright year: 2006
Publisher: Springer
Publication date: 7/24/2006
Binding: Hardcover
Pages: 376
Size: 6.25" wide x 9.25" long x 0.75" tall
Weight: 1.672
Language: English

Historical Foreword
List of Special Symbols
The Order Structure of Positive Operators
Basic Properties of Positive Operators
Extensions of Positive Operators
Order Projections
Order Continuous Operators
Positive Linear Functionals
Components, Homomorphisms, and Orthomorphisms
The Components of a Positive Operator
Lattice Homomorphisms
Topological Considerations
Topological Vector Spaces
Weak Topologies on Banach Spaces
Locally Convex-Solid Riesz Spaces
Banach Lattices
Banach Lattices with Order Continuous Norms
Weak Compactness in Banach Lattices
Embedding Banach Spaces
Banach Lattices of Operators
Compactness Properties of Positive Operators
Compact Operators
Weakly Compact Operators
L- and M-weakly Compact Operators
Dunford-Pettis Operators