Invitation to Operator Theory

This book offers a comprehensive and reader-friendly exposition of the theory of linear operators on Banach spaces and Banach lattices using their topological and order structures and properties. Abramovich and Aliprantis give a unique presentation that includes many new and recent advances in operator theory and brings 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 self-contained 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 presentation. They help to free the proofs of the main results of technical details, which are secondary to the principal ideas, 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, and among them there are many well-known results whose proofs are not readily available elsewhere. Prerequisites are the standard introductory graduate courses in real analysis, general topology, measure theory, and functional analysis. The volume is suitable for graduate or advanced courses in operator theory, real analysis, integration theory, measure theory, function theory, and functional analysis. It will also be of great interest to researchers in mathematics, as well as in physics, economics, finance, engineering, and other related areas. The companion volume, Problems in Operator Theory, containing complete solutions to all exercises in An Invitation to Operator Theory, is available from the AMS as Volume 51 in the Graduate Studies in Mathematics series.