Hilbert Space Operators A Problem Solving Approach [Paperback]

This self-contained work on Hilbert space operators takes a problem-solving approach to the subject, combining theoretical results with a wide variety of exercises that range from the straightforward to the state-of-the-art.  Complete solutions to all problems are provided.  The text covers the basics of bounded linear operators on a Hilbert space and gradually progresses to more advanced topics in spectral theory and quasireducible operators. 

Written in a motivating and rigorous style, the work has few prerequisites beyond elementary functional analysis, and will appeal to graduate students and researchers in mathematics, physics, engineering, and related disciplines.

This is a problem book on Hilbert space operators (Le. , on bounded linear transformations of a Hilbert space into itself) where theory and problems are investigated together. We tre!l:t only a part of the so-called single operator theory. Selected prob? lems, ranging from standard textbook material to points on the boundary of the subject, are organized into twelve chapters. The book begins with elementary aspects of Invariant Subspaces for operators on Banach spaces 1. Basic properties of Hilbert Space Operators are introduced in in Chapter Chapter 2, Convergence and Stability are considered in Chapter 3, and Re? ducing Subspaces is the theme of Chapter 4. Primary results about Shifts on Hilbert space comprise Chapter 5. These are introductory chapters where the majority of the problems consist of auxiliary results that prepare the ground for the next chapters. Chapter 6 deals with Decompositions for Hilbert space contractions, Chapter 7 focuses on Hyponormal Operators, and Chapter 8 is concerned with Spectral Properties of operators on Banach and Hilbert spaces. The next three chapters (as well as Chapter 6) carry their subjects from an introductory level to a more advanced one, including slóâ