The Elements of Operator Theory

This second edition of Elements of Operator Theory is a concept-driven textbook including a significant expansion of the problems and solutions used to illustrate the principles of operator theory. Written in a user-friendly, motivating style intended to avoid the formula-computational approach, fundamental topics are presented in a systematic fashion, i.e., set theory, algebraic structures, topological structures, Banach spaces, and Hilbert spaces, culminating with the Spectral Theorem.

*Key Features include:

*More than 300 fully rigorous proofs, specially tailored to the presentation

*As many as 150 examples, and several interesting counterexamples that demonstrate the frontiers of an important theorem

*Over 300 problems, many with hints, and including 20 pages of additional problems for the second edition

*Both problems and examples underscore further auxiliary results and extensions of the main theory; challenging the reader to prove the principal theorems anew

*This self-contained work is an excellent text for the classroom as well as a self-study resource for researchers. Prerequisites include an introduction to analysis and to functions of a complex variable, which most first-year graduate students in mathematics, engineering, or another formal science have already acquired. Measure theory and integration theory are required only for the last section of the final chapter.

*Review of the first edition:

*"This is a rigorous, logically well-organized textbook presenting basic principles and elementary theory of operators. It is written with great care, gradually increasing in complexity. The forte features of the book are the teaching style, illuminating explanation of numerous delicate points, and detailed presentation of topics. Hence, the book can be warmly recommended to a first work for the study of operator theory . . . it is an admirable work for a modern introduction in operator theory." --Zentralblatt MATH