An Invitation to Operator Theory (Volume 50) and Problems in Operator Theory (Volume 51)Share this page
Y. A. Abramovich; C. C. Aliprantis
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 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 well-known 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
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 self-contained as possible. The best way of learning mathematics is by doing mathematics, and the book
Prerequisites to each book are the standard introductory graduate courses in real analysis, general topology, measure theory, and functional analysis.