HILBERT SPACE OPERATORS: A PROBLEM SOLVING APPROACH

KUBRUSLY,CARLOS

ISBN 10: 0817632425 / ISBN 13: 9780817632427

Published by Birkhaeuser Verlag, 2003

About this Item

This self-contained tatment of bounded linear operators on a Hilbert space provides an examination of the theory from a problem solving viewpoint. Each chapter interweaves theoretical results with a number of problems, ranging from simple yet intructive exercises to open questions at the forefront of current research; complete solutions to all stated problems are provided. Written in a motivating and rigorous style, the text covers much of the classical theory, it beging with the basics of invariant subspaces, linear operator, convergence, shifts, anddecompositions, and then proceeds to hyponormal operators. The book concludes with a detailed presentation of the Lomonosov hrorem on nontrivial hyperinvariant subspaces for compact operators. Some Knowledge of elementary functional anaylisi and familiarity with the basics of operator theory are all that is required. While this problem solving approach to the study of Hilbert space operators is primarily aimed at gratuate students, it will benefit researchers and working scientists as well, given the far-reaching applications of the subject to pire and applied mathematics, physics, engineering, ecnomics, and statistics. 300 gr.

Seller Inventory # 9780817632427LEA45950

Bibliographic Details

• Title: HILBERT SPACE OPERATORS: A PROBLEM SOLVING APPROACH
• Publisher: Birkhaeuser Verlag
• Publication Date: 2003
• Language: English
• ISBN 10: 0817632425
• ISBN 13: 9780817632427
• Binding: Blanda
• Illustrator: No Aplica
• Edition: 0.
• Condition: New
• Dust Jacket Condition: Nuevo
• Book Type: Libro

About this title

Synopsis

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 some recent results. Chapter 9 is about Paranormal Operators, Chapter 10 covers Proper Contractions, and Chapter 11 searches through Quasi­ reducible Operators. The final Chapter 12 commemorates three decades of The Lomonosov Theorem on nontrivial hyperinvariant subspaces for compact operators.

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