Hardcover ISBN:  9780821821466 
Product Code:  GSM/50 
List Price:  $90.00 
MAA Member Price:  $81.00 
AMS Member Price:  $72.00 
Electronic ISBN:  9781470420994 
Product Code:  GSM/50.E 
List Price:  $84.00 
MAA Member Price:  $75.60 
AMS Member Price:  $67.20 

Book DetailsGraduate Studies in MathematicsVolume: 50; 2002; 530 ppMSC: Primary 46; 47; 28; 15;
This book offers a comprehensive and readerfriendly exposition of the theory of linear operators on Banach spaces and Banach lattices. Abramovich and Aliprantis give a unique presentation that includes many new developments in operator theory and also draws together results that are spread over the vast literature. For instance, invariant subspaces of positive operators and the Daugavet equation are presented in monograph form for the first time.
The authors keep the discussion selfcontained and use exercises to achieve this goal. The book contains over 600 exercises to help students master the material developed in the text. The exercises are of varying degrees of difficulty and play an important and useful role in the exposition. They help to free the proofs of the main results of some technical details but provide students with accurate and complete accounts of how such details ought to be worked out. The exercises also contain a considerable amount of additional material that includes many wellknown results whose proofs are not readily available elsewhere.
The companion volume, Problems in Operator Theory, also by Abramovich and Aliprantis, is available from the AMS as Volume 51 in the Graduate Studies in Mathematics series, and it contains complete solutions to all exercises in An Invitation to Operator Theory.
The solutions demonstrate explicitly technical details in the proofs of many results in operator theory, providing the reader with rigorous and complete accounts of such details. Finally, the book offers a considerable amount of additional material and further developments. By adding extra material to many exercises, the authors have managed to keep the presentation as selfcontained as possible. The best way of learning mathematics is by doing mathematics, and the book Problems in Operator Theory will help achieve this goal.
Prerequisites to each book are the standard introductory graduate courses in real analysis, general topology, measure theory, and functional analysis. An Invitation to Operator Theory is suitable for graduate or advanced courses in operator theory, real analysis, integration theory, measure theory, function theory, and functional analysis. Problems in Operator Theory is a very useful supplementary text in the above areas. Both books will be of great interest to researchers and students in mathematics, as well as in physics, economics, finance, engineering, and other related areas, and will make an indispensable reference tool.ReadershipGraduate students and researchers interested in mathematics, physics, economics, finance, engineering, and other related areas.
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Table of Contents

Chapters

Chapter 1. Odds and ends

Chapter 2. Basic operator theory

Chapter 3. Operators on $AL$ and $AM$spaces

Chapter 4. Special classes of operators

Chapter 5. Integral operators

Chapter 6. Spectral properties

Chapter 7. Some special spectra

Chapter 8. Positive matrices

Chapter 9. Irreducible operators

Chapter 10. Invariant subspaces

Chapter 11. The Daugavet equation


Additional Material

Reviews

The book is a fine introduction to this particular part of operator theory … In addition to the choice of material and the book being as wellwritten as one normally expects from these authors … there are two features that set this book apart from others. The first is the great care that the authors give to correct attribution of original results … and the second is the exercises that are included … there are over 600 exercises … The authors take the same care with the attribution of these exercises as they do with the results in the body of the text … one could hardly wish for a better text than this one.
Mathematical Reviews


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This book offers a comprehensive and readerfriendly exposition of the theory of linear operators on Banach spaces and Banach lattices. Abramovich and Aliprantis give a unique presentation that includes many new developments in operator theory and also draws together results that are spread over the vast literature. For instance, invariant subspaces of positive operators and the Daugavet equation are presented in monograph form for the first time.
The authors keep the discussion selfcontained and use exercises to achieve this goal. The book contains over 600 exercises to help students master the material developed in the text. The exercises are of varying degrees of difficulty and play an important and useful role in the exposition. They help to free the proofs of the main results of some technical details but provide students with accurate and complete accounts of how such details ought to be worked out. The exercises also contain a considerable amount of additional material that includes many wellknown results whose proofs are not readily available elsewhere.
The companion volume, Problems in Operator Theory, also by Abramovich and Aliprantis, is available from the AMS as Volume 51 in the Graduate Studies in Mathematics series, and it contains complete solutions to all exercises in An Invitation to Operator Theory.
The solutions demonstrate explicitly technical details in the proofs of many results in operator theory, providing the reader with rigorous and complete accounts of such details. Finally, the book offers a considerable amount of additional material and further developments. By adding extra material to many exercises, the authors have managed to keep the presentation as selfcontained as possible. The best way of learning mathematics is by doing mathematics, and the book Problems in Operator Theory will help achieve this goal.
Prerequisites to each book are the standard introductory graduate courses in real analysis, general topology, measure theory, and functional analysis. An Invitation to Operator Theory is suitable for graduate or advanced courses in operator theory, real analysis, integration theory, measure theory, function theory, and functional analysis. Problems in Operator Theory is a very useful supplementary text in the above areas. Both books will be of great interest to researchers and students in mathematics, as well as in physics, economics, finance, engineering, and other related areas, and will make an indispensable reference tool.
Graduate students and researchers interested in mathematics, physics, economics, finance, engineering, and other related areas.

Chapters

Chapter 1. Odds and ends

Chapter 2. Basic operator theory

Chapter 3. Operators on $AL$ and $AM$spaces

Chapter 4. Special classes of operators

Chapter 5. Integral operators

Chapter 6. Spectral properties

Chapter 7. Some special spectra

Chapter 8. Positive matrices

Chapter 9. Irreducible operators

Chapter 10. Invariant subspaces

Chapter 11. The Daugavet equation

The book is a fine introduction to this particular part of operator theory … In addition to the choice of material and the book being as wellwritten as one normally expects from these authors … there are two features that set this book apart from others. The first is the great care that the authors give to correct attribution of original results … and the second is the exercises that are included … there are over 600 exercises … The authors take the same care with the attribution of these exercises as they do with the results in the body of the text … one could hardly wish for a better text than this one.
Mathematical Reviews