Hilbert Space Operators: A Problem Solving Approach

Hilbert Space Operators: A Problem Solving Approach

This self-contained work on Hilbert space operators takes a problem-solving approach to the subject, combining theoretical results with??ide variety of?xercises that range from the?traightforward to the state-of-the-art.?Complete solutions to all?roblems 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.Review"?the author treats many new subjects of operator theory for graduate students and mathematicians, i.e., quasihyponormal operators, paranormal operators, proper contractions, quasireducible operators, a detailed presentation of the Lomonosov theorem on nontrivial hyperinvariant subspaces for compact operators, etc. This book will be of benefit to graduate students (in mathematics, physics, engineering, economics, and statistics) and many mathematicians." ?Zentralblatt MATH"?many totally new subjects are offered to the potential reader?. The author has great teaching experience reflected by the skillful selection of background material, the gradual statements of the problems, and the detailed presentation of the solutions. The book is intended [for] an audience mainly formed by various types of graduate students: in mathematics, statistics, physics and, perhaps, in engineering and economics. It can be useful even for working mathematicians, as a reference book in a broad sense?."?Mathematical Reviews